RADIO NUMBER FOR CROSS PRODUCT P n (P 2 ) Gyeongsang National University Jinju, , KOREA 2,4 Department of Mathematics
|
|
- Justina Casey
- 5 years ago
- Views:
Transcription
1 Iteratioal Joural of Pure ad Applied Mathematics Volume 97 No , ISSN: (prited versio); ISSN: (o-lie versio) url: doi: PAijpam.eu RADIO NUMBER FOR CROSS PRODUCT P (P ) Chah Yog Jug 1, Waqas Nazeer, Saima Nazeer 3, Arif Rafiq 4 ad Shi Mi Kag 5 1 Departmet of Busiess Admiistratio Gyeogsag Natioal Uiversity Jiju, , KOREA,4 Departmet of Mathematics Lahore Leads Uiversity Lahore, 54810, PAKISTAN 3 Departmet of Mathematics Lahore College for Wome Uiversity Lahore, 54600, PAKISTAN 5 Departmet of Mathematics ad RINS Gyeogsag Natioal Uiversity Jiju, , KOREA Abstract: A Radio labelig of the graph G is a fuctio g from the vertex set V(G) of G to N {0} such that f(u) f(v) diam(g)+1 d G (u,v), where diam(g) ad d G (u,v) are diameter ad distace betwee u ad v i graph G, respectively. The radio umber r(g) of G is the smallest umber k such that G has radio labelig with max{f(v) : v V(G)} = k. We ivestigate radio umber for the cross product of P ad P. AMS Subject Classificatio: 05C1, 05C15, 05C78 Key Words: chael assigmet, radio labelig, radio umber, cross product Received: August 8, 014 Correspodece author c 014 Academic Publicatios, Ltd. url:
2 516 C.Y. Jug et al 1. Itroductio I 1980, Hale [5] preseted the idea for radio frequecy assigmet problems. Later i 001, Chartrad et al. [] applied this idea for assigmet of chaels to FM radio statio. These assigmet have bee made o the fact that frequecies eed to be assiged to the chaels such that there is miimum iterferece. The geographically closed radio statios should be assiged differet frequecies to avoid iterferece. The iterferece graph is developed to solve the chaels assigmet problems by covertig a assigmet of chaels i to graph labelig. I iterferece graph, there is a edge betwee two vertices if the correspodig trasmitter have major iterferece. It is assumed that the distace betwee vertices is two if two trasmitters have mior iterferece i iterferece graph ad if the vertices are at distace three or beyod the there is o iterferece betwee trasmitters. I other words, the adjacet vertices represet the very close trasmitters ad those vertices which are at distace two apart represets close trasmitters. A pair of trasmitters which has small iterferece must receive differet chaels ad two trasmitters which has large iterferece must receive chaels that are at least two apart are suggested i [1] by Robert. Motivated through this problem Griggs ad Yeh [4] relates the chaels with o-egative iteger by itroducig L(, 1)-labelig, which is defied as follows: Defiitio 1.1. A distace two labelig (or L(, 1)-labelig) of a graph G = (V(G),E(G)) isafuctiogfromvertex set V(G) tothesetofoegative itegers such that the followig coditios are satisfied: (1) g(u) g(v) if d(u,v) = 1, () g(u) g(v) 1 if d(u,v) =. The differece betwee the largest ad the smallest label assiged by g is called the spa of g ad the miimum spa over all L(,1)-labelig of G is called the λ-umber of G, deoted by λ(g). The L(, 1)-labelig has explored i the past two decades by may researchers like Chag ad Kuo [1], Georges ad Mauro [3], Sabaki [13], Vaidya ad Batva [14], Vaidya et al. [16], Wag [17] ad Yeh [18], [19]. But as time passed, practically it has bee observed that the iterferece amog trasmitters might go beyod two levels. Radio labelig exteds the umber of iterferece level cosidered i L(, 1)-labelig from two to largest possible iterferece amog trasmitter, i.e. the diameter of G which is defied
3 RADIO NUMBER FOR CROSS PRODUCT P (P ) 517 as follows: Defiitio 1.. The diameter of a graph is deoted by diam(g) ad defied as the maximum distace betwee ay two vertices, that is, diam(g) = max{d(u,v);u,v G}. Here d(u,v) is distace betwee u ad v which is defied as follows: Defiitio 1.3. Let G be a coected graph, the distace d(u,v) betwee ay pair of vertices u,v is the legth of the shortest path betwee them. Motivated through the problem of chael assigmet of FM radio statios Chartrad et al. [] itroduced the cocept of radio labelig which also kow as Multi-level distace labelig of graph as follows: Defiitio 1.4. A radio labelig which is also kow as multilevel distace labelig of G is a fuctio g : V(G) N {0} such that the iequality g(u) g(v) diam(g)+1 d(u,v) holds for ay pair of distict vertices u,v. The spa of g is the differece of the largest ad the smallest chaels used, max u,v V(G) {g(v) g(u)}. The radio umber of G is deoted by r(g) ad is defied as the miimum spa of radio labelig of G. Note that whe diam(g) is two tha radio labelig ad distace two labelig are idetical. The radio labelig is studied i the past decade by may researches like Liu [6], Liu ad Xie [7], [8], Liu ad Zhu [9] ad Vaidya ad Vihol [15]. Moreover, the radio umber for path ad cycles was determied i [9], for the square of paths was ivestigated by Liu ad Xie [8], for the square of a cycle [7]. Radio Number for geeralized prism graph was studied i [10] ad a geeralized gear graph was discussed i [11], where lower boud of radio umber is determied. Radio labelig for some cycle related graphs are studied by Vadiya ad Vihol [15]. I this paper, we completely determie the radio umber of cross product for P ad P. Through our this discussio, the order of P (P ) is. I Theorem. we determie the radio umber for P (P ). Theorem.3 ad Theorem.5 give us lower ad upper boud for radio umber of P (P ); 3, ad fially i Theorem.6 we get r(p (P )) = +1.. Mai Results The cross product of graphs G ad H deoted by G(H), is the graph with the vertex set V(G) V(H) = {(u,v) : u V(G), v V(H)}, where (u,x)
4 518 C.Y. Jug et al is adjacet to (v,y) wheever (i) u 1 = v 1 ad u v or (ii) u 1 v 1 ad u v. Case 1: For P (P ), whe is odd, let v 0 ad u 0 be the ceters. Let v 1,v,,v 1 be the vertices o the left side ad v 1,v,,v 1 be the vertices o the right side with respect to ceter v 0 ad u 1,u,,u 1 vertices o the left side ad u 1,u,,u 1 with respect to ceter u 0. So for P (P ), V(P (P )) = V V U U, where V = {v 0,v 1,v,,v 1 U = {u 0,u 1,u,,u 1 be the be the vertices o the right side }, V = {v 0,v 1,v,,v 1}, }, U = {u 0,u 1,u,,u 1 Case : For P (P ), whe is eve, let v 0 ad v 0, u 0 ad u 0 bethe ceters. Let v 1,v,,v 1 be the vertices o the left side with respect to ceter v 0 ad v 1,v,,v 1 be the vertices o the right side with respect to ceter v 0 ad u 1,u,,u 1 be the vertices o the left side with respect to ceter u 0 ad u 1,u,,u 1 be the vertices o the right side with respect to ceter u 0. So for P (P ), V(P (P )) = V V U U, where V = {v 0,v 1,v,,v 1 }, V = {v 0,v 1,v,...,v 1}, U = {u 0,u 1,u,...,u 1 }, U = {u 0,u 1,u,,u 1}. We say two vertices u ad v are o opposite side i P (P ), if u V V ad v U U. Defiitio.1. Thelevel fuctio l from V(P (P )) to set of oegative itegers from a ceter vertex c is defied as l(u) := {d(u,c);c is a ceter vertex} for ay u V(P (P )). Note that, i P (P ), the maximum level fuctio is 1 if is odd ad 1 if is eve. Observatios. We made followig observatio for P (P ), }. (a) (b) d(u,v) V(P (P )) = { l(u)+l(v), if is odd; l(u)+l(v)+1, if is eve.
5 RADIO NUMBER FOR CROSS PRODUCT P (P ) 519 Theorem.. Let P (P ) be the cross product of P ad P. The r(p (P )) = 4. Proof. Radio labelig of P (P ) as show i figure Figure 1: r(p (P )) = 4 Theorem.3. Let P (P ) be the cross product of P ad P for 3. The r(p (P )) +1. Moreover, the equality holds if ad oly if there exist a radio labelig g with orderig u 1,u,..., of vertices of P (P ) such that g(u 1 ) = 0 < g(u ) < g(u 3 ) < < g(u ), all the followig holds, for all 1 i 1, (a) u i ad u i+1 are o opposite sides, (b) {u 1,u } = {c 1,c }, where c 1,c are ceter vertices. The Proof. Let g be a optimal radio labelig for P (P ), where g(u 1 ) = 0 < g(u ) < g(u 3 ) < < g(u ). g(u i+1 ) g(u i ) (d+1) d(u i,u i+1 ) for all 1 i 1. Summig these 1 iequalities, we get 1 r(p (P )) = g(u ) ( 1)(d+1) d(u i,u i+1 ) (.1) i=1
6 50 C.Y. Jug et al Case (a): For P (P ), whe is odd, we have 1 i=1 d(u i,u i+1 ) [l(u i )+l(u i+1 )] 1 i=1 = u V (G) u V (G) l(u) l(u 1 ) l(u ) l(u). (.) Substitutig (.) i (.1), we get r(p (P )) = g(u ) ( 1)(d+1) u V(G) l(u), sice d = 1 ad u V(G) l(u) = 1, so ( ) 1 r(p (P )) ( 1)() = +1. Case (b): For P (P ), whe is eve, we have 1 i=1 d(u i,u i+1 ) [l(u i )+l(u i+1 )+1] 1 i=1 = u V(G) u V(G) l(u) l(u 1 ) l(u )+( 1) l(u)+( 1). (.3) Substitutig (.3) i (.1), we get r(p (P )) = g(u ) ( 1)(d+1) u V(G) l(u) ( 1), sice d = 1 ad u V(G) l(u) =, so ( ) r(p (P )) ( 1)() ( 1) = +1. Thus, from above two cases we have desired result.
7 RADIO NUMBER FOR CROSS PRODUCT P (P ) 51 Theorem.4. Let g be a assigmet of distict o-egative itegers to V(P (P )) ad {u 1,u,u 3,,u } be the orderig of V(P (P )) such that g(u i ) < g(u i+1 ) defied by g(u 1 ) = 0 ad g(u i+1 ) = g(u i )+d+1 d(u i,u i+1 ). The g is a radio labelig ad for ay 1 i, the followig holds. (a) d(u i,u i+1 ) +1 if is odd, (b) d(u i,u i+1 ) +1 ad d(u i,u i+1 ) d(u i+1,u i+ ) if is eve. Proof. Let g(u 1 ) = 0 ad g(u i+1 ) = g(u i ) + d + 1 d(u i,u i+1 ), for ay 1 i 1, ad let for each i = 1,,..., 1, g i = g(u i+1 ) g(u i ). We wat to prove that g is a radio labelig, if (a) ad (b) holds, that is, for ay j i, g(u j ) g(u i ) d+1 d(u j,u i ) Case (a): Whe is odd, we have d = 1 ad let (a) holds ad we take i > j, the g(u i ) g(u j ) = g j +g j+1 + +g i 1 = (i j)(d+1) d(u j,u j+1 ) d(u j+1,u j+ ) d(u i 1,u i ) ( ) +1 (i j)() (i j) by usig (1) ( ( )) +1 = (i j) ( ) 1 = (i j) d+1 d(u i,u j ). Case (b): Whe is eve, let (b) holds ad we take i > j g(u i ) g(u j ) = g j +g j+1 + +g i 1 = (i j)(d+1) d(u j,u j+1 ) d(u j+1,u j+ ) d(u i 1,u i )
8 5 C.Y. Jug et al If i j = eve, the If i j = odd, the g(u i ) g(u j ) (i j)(d+1) i j ( ) +1 ( ) = (i j)() (i j) i j ( ) = (i j) i j d+1 d(u i,u j ). g(u i ) g(u j ) (i j)(d+1) d+1 d(u i,u j ). ( ) i j i j ( ) i j +1 ( ) Thus, i both the cases g is a radio labelig ad hece the result. Theorem.5. Let P (P ) be the cross product of P ad P for 3. The r(p (P )) +1. Proof. Here we cosider followig two cases. Case 1: Whe is odd, defie g : V(P (P )) {0,1,,..., +1} by g(u i+1 ) = g(u i )+d+1 l(u i ) l(u i+1 ) as per orderig of vertices give below v Rk v L1 v Rk v L1 v R(k 1) 1 v v L v R(k 1) v Lk v R1 +1 v Lk +1 v L 1 1 v 0 1 v R1 Case : Whe is eve, defie g : V(P (P )) {0,1,,..., +1} by
9 RADIO NUMBER FOR CROSS PRODUCT P (P ) 53 g(u i+1 ) = g(u i )+d l(u i ) l(u i+1 ) as per orderig of vertices give below. v L0 + v R(k 1) + v R(k 3) v R(k 1) + v L1 + v L1 + v L(k 1) v R(k ) + + v L 1 v L(k 1) v R0 v L0 v R(k ) v R0 + v L v R(k 3) Sice g satisfy coditios of Theorem.4, so g is radio labelig with spa +1, hece r(p (P )) +1. Theorem.6. Let P (P ) be the cross product of P ad P. The r(p (P )) = +1. Proof. The proof follows from Theorem.3 ad Theorem.5. Example.7. I Figure, orderig of the vertices ad optimal radio labelig of P 9 (P ) is show. v 0 v 4 v 1 u 4 u 1 v 3 v u 3 u v v 3 u u 3 v 1 v 4 u 1 u 4 u 0 = r(p 9 (P )). u4 u u 3 u1 u u 1 u u 3 u v4 v3 v v v 1 0 v 1 v v 3 v 4 Figure : r(p 9 (P ) = 73
10 54 C.Y. Jug et al Example.8. I Figure 3, orderig of the vertices ad optimal radio labelig of P 10 (P ) is show v 0 v 4 v 1 v 3 v v v 3 v 1 v 4 v 0 u 0 u 4 u 1 u 3 v u u 3 u 1 u 4 u 0 = r(p 10 (P )). u 4 u u u1 u0 u u 1 u 8 73 u 3 u v 4 v v3 0 v v v 0 v v v 3 5 v 4 Figure 3: r(p 10 (P )) = 91 Refereces [1] G.J. Chag, D. Kuo, The L(, 1)-labelig problem o graphs, SIAM J. Discrete Math., 9 (1996), [] G. Chartrad, D. Erwi, P. Zhag, F. Harary, Radio labeligs of graphs, Bull. Ist. Combi. Appl., 33 (001), [3] J.P. Georges, D.W. Mauro, Labelig trees with coditio at distace two, Discrete Math., 69 (003), , doi: /S X(0) [4] J.R. Griggs, R.K. Yeh, Labelig graphs with coditio at distace, SIAM J. Discrete Math., 5 (199), [5] W.K. Hale, Frequecy assigemet: theory ad applicatio, Proc. IEEE, 68 (1980), [6] D.D.F. Liu, Radio umber for trees, Discrete Math., 308 (008), , doi: /j.disc
11 RADIO NUMBER FOR CROSS PRODUCT P (P ) 55 [7] D.D.F. Liu, M. Xie, Radio umber for square cycles, Cogr. Numer., 169 (004), [8] D.D.F. Liu, M. Xie, Radio umber for square paths, Ars Combi., 90 (009), [9] D.D.F. Liu, X. Zhu, Multi-level distace labelig for paths ad cycles, SIAM J. Discrete Math., 19 (005), [10] P. Martiez, J. Ortiz, M. Tomova, C. Wyels, Radio umbers for geeralized prism graphs, Discuss Math. Graph Theory, 31 (011), [11] M.T. Rahim, M. Farooq, M. Ali, S. Ja, Multi-level distace labeligs for geeralized gear graph, It. J. Math. Soft Comput., (01), [1] F.S. Roberts, T-colorig of graphs: recet results ad ope problems, Discrete Math., 93 (1991), 9-45, doi: / X(91) [13] D. Sakai, Labelig chordal: distace two coditio, SIAM J. Discrete Math., 7 (1994), [14] S.K. Vaidya, D.D. Batva, Labelig cacti with a coditio at distace two, Le Matematiche, 66 (011), [15] S.K. Vaidya, P.L. Vihol, Radio labelig for some cycle related graphs, It. J. Math. Soft Comput., (01), [16] S.K. Vaidya, P.L. Vihol, N.A. Dai, D.D. Batva, L(, 1)-labelig i the cotexamplet of some graph operatios, J. Math. Res., (010), [17] W.F. Wag, The L(, 1)-labelig of trees, Discrete Appl. Math., 154 (006), , doi: /j.dam [18] R.K. Yeh, Labelig Graphs with a Coditio at Distace Two, Ph.D. Thesis, Departmet of Mathematics, Uiversoty of South Carolia, Columbia, South Carolia, [19] R.K. Yeh, A survey o labelig graphs with coditio at distace two, Discrete Math., 306 (006), , doi: /j.disc
12 56
ON RADIO NUMBER OF STACKED-BOOK GRAPHS arxiv: v1 [math.co] 2 Jan 2019
ON RADIO NUMBER OF STACKED-BOOK GRAPHS arxiv:1901.00355v1 [math.co] Ja 019 TAYO CHARLES ADEFOKUN 1 AND DEBORAH OLAYIDE AJAYI Abstract. A Stacked-book graph G m, results from the Cartesia product of a stargraphs
More informationPAijpam.eu IRREGULAR SET COLORINGS OF GRAPHS
Iteratioal Joural of Pure ad Applied Mathematics Volume 109 No. 7 016, 143-150 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://www.ijpam.eu doi: 10.173/ijpam.v109i7.18 PAijpam.eu
More informationγ-max Labelings of Graphs
γ-max Labeligs of Graphs Supapor Saduakdee 1 & Varaoot Khemmai 1 Departmet of Mathematics, Sriakhariwirot Uiversity, Bagkok, Thailad Joural of Mathematics Research; Vol. 9, No. 1; February 017 ISSN 1916-9795
More informationEQUITABLE DOMINATING CHROMATIC SETS IN GRAPHS. Sethu Institute of Technology Kariapatti, Tamilnadu, INDIA 2 Department of Mathematics
Iteratioal Joural of Pure ad Applied Mathematics Volume 104 No. 2 2015, 193-202 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v104i2.4
More informationk-equitable mean labeling
Joural of Algorithms ad Comutatio joural homeage: htt://jac.ut.ac.ir k-euitable mea labelig P.Jeyathi 1 1 Deartmet of Mathematics, Govidammal Aditaar College for Wome, Tiruchedur- 628 215,Idia ABSTRACT
More informationWeakly Connected Closed Geodetic Numbers of Graphs
Iteratioal Joural of Mathematical Aalysis Vol 10, 016, o 6, 57-70 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/101988/ijma01651193 Weakly Coected Closed Geodetic Numbers of Graphs Rachel M Pataga 1, Imelda
More informationL(3,2,1)-and L(4,3,2,1)-labeling Problems on Circular-ARC Graphs
I J C T, 9(34) 016, pp. 869-884 Iteratioal Sciece Press L(3,,1)-ad L(4,3,,1)-labelig Problems o Circular-RC Graphs S maathulla * ad Madhumagal Pal * BSTRCT For a give graph G ( V, E), the L(3,,1) - ad
More informationRandić index, diameter and the average distance
Radić idex, diameter ad the average distace arxiv:0906.530v1 [math.co] 9 Ju 009 Xueliag Li, Yogtag Shi Ceter for Combiatorics ad LPMC-TJKLC Nakai Uiversity, Tiaji 300071, Chia lxl@akai.edu.c; shi@cfc.akai.edu.c
More informationAbsolutely Harmonious Labeling of Graphs
Iteratioal J.Math. Combi. Vol. (011), 40-51 Absolutely Harmoious Labelig of Graphs M.Seeivasa (Sri Paramakalyai College, Alwarkurichi-6741, Idia) A.Lourdusamy (St.Xavier s College (Autoomous), Palayamkottai,
More informationAdjacent vertex distinguishing total coloring of tensor product of graphs
America Iteratioal Joural of Available olie at http://wwwiasiret Research i Sciece Techology Egieerig & Mathematics ISSN Prit): 38-3491 ISSN Olie): 38-3580 ISSN CD-ROM): 38-369 AIJRSTEM is a refereed idexed
More informationRadio Number for Square Paths
Radio Number for Square Paths Daphne Der-Fen Liu Department of Mathematics California State University, Los Angeles Los Angeles, CA 9003 Melanie Xie Department of Mathematics East Los Angeles College Monterey
More informationBi-Magic labeling of Interval valued Fuzzy Graph
Advaces i Fuzzy Mathematics. ISSN 0973-533X Volume 1, Number 3 (017), pp. 645-656 Research Idia Publicatios http://www.ripublicatio.com Bi-Magic labelig of Iterval valued Fuzzy Graph K.Ameeal Bibi 1 ad
More informationPAijpam.eu ON TENSOR PRODUCT DECOMPOSITION
Iteratioal Joural of Pure ad Applied Mathematics Volume 103 No 3 2015, 537-545 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://wwwijpameu doi: http://dxdoiorg/1012732/ijpamv103i314
More informationMath 778S Spectral Graph Theory Handout #3: Eigenvalues of Adjacency Matrix
Math 778S Spectral Graph Theory Hadout #3: Eigevalues of Adjacecy Matrix The Cartesia product (deoted by G H) of two simple graphs G ad H has the vertex-set V (G) V (H). For ay u, v V (G) ad x, y V (H),
More informationThe Multiplicative Zagreb Indices of Products of Graphs
Iteratioal Joural of Mathematics Research. ISSN 0976-5840 Volume 8, Number (06), pp. 6-69 Iteratioal Research Publicatio House http://www.irphouse.com The Multiplicative Zagreb Idices of Products of Graphs
More informationBertrand s Postulate
Bertrad s Postulate Lola Thompso Ross Program July 3, 2009 Lola Thompso (Ross Program Bertrad s Postulate July 3, 2009 1 / 33 Bertrad s Postulate I ve said it oce ad I ll say it agai: There s always a
More informationOn size multipartite Ramsey numbers for stars versus paths and cycles
Electroic Joural of Graph Theory ad Applicatios 5 (1) (2017), 4 50 O size multipartite Ramsey umbers for stars versus paths ad cycles Aie Lusiai 1, Edy Tri Baskoro, Suhadi Wido Saputro Combiatorial Mathematics
More informationCHAPTER 2 NEIGHBORHOOD CONNECTED PERFECT DOMINATION IN GRAPHS
22 CHAPTER 2 NEIGHBORHOOD CONNECTED PERFECT DOMINATION IN GRAPHS 2.1 INTRODUCTION Various types of domiatio have bee studied by several authors ad more tha 75 models of domiatio are listed i the appedix
More informationThe Local Harmonious Chromatic Problem
The 7th Workshop o Combiatorial Mathematics ad Computatio Theory The Local Harmoious Chromatic Problem Yue Li Wag 1,, Tsog Wuu Li ad Li Yua Wag 1 Departmet of Iformatio Maagemet, Natioal Taiwa Uiversity
More informationMultilevel Distance Labelings for Paths and Cycles
Multilevel Distance Labelings for Paths and Cycles Daphne Der-Fen Liu Department of Mathematics California State University, Los Angeles Los Angeles, CA 90032, USA Email: dliu@calstatela.edu Xuding Zhu
More informationUnsaturated Solutions of A Nonlinear Delay Partial Difference. Equation with Variable Coefficients
Europea Joural of Mathematics ad Computer Sciece Vol. 5 No. 1 18 ISSN 59-9951 Usaturated Solutios of A Noliear Delay Partial Differece Euatio with Variable Coefficiets Xiagyu Zhu Yuahog Tao* Departmet
More informationPAijpam.eu ON DERIVATION OF RATIONAL SOLUTIONS OF BABBAGE S FUNCTIONAL EQUATION
Iteratioal Joural of Pure ad Applied Mathematics Volume 94 No. 204, 9-20 ISSN: 3-8080 (prited versio); ISSN: 34-3395 (o-lie versio) url: http://www.ijpam.eu doi: http://dx.doi.org/0.2732/ijpam.v94i.2 PAijpam.eu
More informationRank Modulation with Multiplicity
Rak Modulatio with Multiplicity Axiao (Adrew) Jiag Computer Sciece ad Eg. Dept. Texas A&M Uiversity College Statio, TX 778 ajiag@cse.tamu.edu Abstract Rak modulatio is a scheme that uses the relative order
More informationCommutativity in Permutation Groups
Commutativity i Permutatio Groups Richard Wito, PhD Abstract I the group Sym(S) of permutatios o a oempty set S, fixed poits ad trasiet poits are defied Prelimiary results o fixed ad trasiet poits are
More informationAlliance Partition Number in Graphs
Alliace Partitio Number i Graphs Lida Eroh Departmet of Mathematics Uiversity of Wiscosi Oshkosh, Oshkosh, WI email: eroh@uwoshedu, phoe: (90)44-7343 ad Ralucca Gera Departmet of Applied Mathematics Naval
More informationFuzzy Shortest Path with α- Cuts
Iteratioal Joural of Mathematics Treds ad Techology (IJMTT) Volume 58 Issue 3 Jue 2018 Fuzzy Shortest Path with α- Cuts P. Sadhya Assistat Professor, Deptt. Of Mathematics, AIMAN College of Arts ad Sciece
More informationThe Random Walk For Dummies
The Radom Walk For Dummies Richard A Mote Abstract We look at the priciples goverig the oe-dimesioal discrete radom walk First we review five basic cocepts of probability theory The we cosider the Beroulli
More informationDominating Sets and Domination Polynomials of Square Of Cycles
IOSR Joural of Mathematics IOSR-JM) ISSN: 78-78. Volume 3, Issue 4 Sep-Oct. 01), PP 04-14 www.iosrjourals.org Domiatig Sets ad Domiatio Polyomials of Square Of Cycles A. Vijaya 1, K. Lal Gipso 1 Assistat
More information# fixed points of g. Tree to string. Repeatedly select the leaf with the smallest label, write down the label of its neighbour and remove the leaf.
Combiatorics Graph Theory Coutig labelled ad ulabelled graphs There are 2 ( 2) labelled graphs of order. The ulabelled graphs of order correspod to orbits of the actio of S o the set of labelled graphs.
More informationOn Orlicz N-frames. 1 Introduction. Renu Chugh 1,, Shashank Goel 2
Joural of Advaced Research i Pure Mathematics Olie ISSN: 1943-2380 Vol. 3, Issue. 1, 2010, pp. 104-110 doi: 10.5373/jarpm.473.061810 O Orlicz N-frames Reu Chugh 1,, Shashak Goel 2 1 Departmet of Mathematics,
More informationBI-INDUCED SUBGRAPHS AND STABILITY NUMBER *
Yugoslav Joural of Operatios Research 14 (2004), Number 1, 27-32 BI-INDUCED SUBGRAPHS AND STABILITY NUMBER * I E ZVEROVICH, O I ZVEROVICH RUTCOR Rutgers Ceter for Operatios Research, Rutgers Uiversity,
More informationThe 4-Nicol Numbers Having Five Different Prime Divisors
1 2 3 47 6 23 11 Joural of Iteger Sequeces, Vol. 14 (2011), Article 11.7.2 The 4-Nicol Numbers Havig Five Differet Prime Divisors Qiao-Xiao Ji ad Mi Tag 1 Departmet of Mathematics Ahui Normal Uiversity
More informationSequences A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence
Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece 1, 1, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet
More informationPairs of disjoint q-element subsets far from each other
Pairs of disjoit q-elemet subsets far from each other Hikoe Eomoto Departmet of Mathematics, Keio Uiversity 3-14-1 Hiyoshi, Kohoku-Ku, Yokohama, 223 Japa, eomoto@math.keio.ac.jp Gyula O.H. Katoa Alfréd
More informationIt is always the case that unions, intersections, complements, and set differences are preserved by the inverse image of a function.
MATH 532 Measurable Fuctios Dr. Neal, WKU Throughout, let ( X, F, µ) be a measure space ad let (!, F, P ) deote the special case of a probability space. We shall ow begi to study real-valued fuctios defied
More informationarxiv: v1 [math.co] 29 Jul 2010
RADIO NUMBERS FOR GENERALIZED PRISM GRAPHS PAUL MARTINEZ, JUAN ORTIZ, MAGGY TOMOVA, AND CINDY WYELS arxiv:1007.5346v1 [math.co] 29 Jul 2010 Abstract. A radio labeling is an assignment c : V (G) N such
More informationFLUID LIMIT FOR CUMULATIVE IDLE TIME IN MULTIPHASE QUEUES. Akademijos 4, LT-08663, Vilnius, LITHUANIA 1,2 Vilnius University
Iteratioal Joural of Pure ad Applied Mathematics Volume 95 No. 2 2014, 123-129 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v95i2.1
More informationLarge holes in quasi-random graphs
Large holes i quasi-radom graphs Joaa Polcy Departmet of Discrete Mathematics Adam Mickiewicz Uiversity Pozań, Polad joaska@amuedupl Submitted: Nov 23, 2006; Accepted: Apr 10, 2008; Published: Apr 18,
More informationLONG SNAKES IN POWERS OF THE COMPLETE GRAPH WITH AN ODD NUMBER OF VERTICES
J Lodo Math Soc (2 50, (1994, 465 476 LONG SNAKES IN POWERS OF THE COMPLETE GRAPH WITH AN ODD NUMBER OF VERTICES Jerzy Wojciechowski Abstract I [5] Abbott ad Katchalski ask if there exists a costat c >
More informationFIXED POINTS OF n-valued MULTIMAPS OF THE CIRCLE
FIXED POINTS OF -VALUED MULTIMAPS OF THE CIRCLE Robert F. Brow Departmet of Mathematics Uiversity of Califoria Los Ageles, CA 90095-1555 e-mail: rfb@math.ucla.edu November 15, 2005 Abstract A multifuctio
More informationOn the fractional chromatic number, the chromatic number, and graph products
O the fractioal chromatic umber, the chromatic umber, ad graph products Sadi Klavžar 1 Departmet of Mathematics, PEF, Uiversity of Maribor, Koroška cesta 160, 2000 Maribor, Sloveia e-mail: sadi.klavzar@ui-lj.si
More informationNew Inequalities For Convex Sequences With Applications
It. J. Ope Problems Comput. Math., Vol. 5, No. 3, September, 0 ISSN 074-87; Copyright c ICSRS Publicatio, 0 www.i-csrs.org New Iequalities For Covex Sequeces With Applicatios Zielaâbidie Latreuch ad Beharrat
More informationProperties of Fuzzy Length on Fuzzy Set
Ope Access Library Joural 206, Volume 3, e3068 ISSN Olie: 2333-972 ISSN Prit: 2333-9705 Properties of Fuzzy Legth o Fuzzy Set Jehad R Kider, Jaafar Imra Mousa Departmet of Mathematics ad Computer Applicatios,
More informationDisjoint unions of complete graphs characterized by their Laplacian spectrum
Electroic Joural of Liear Algebra Volume 18 Volume 18 (009) Article 56 009 Disjoit uios of complete graphs characterized by their Laplacia spectrum Romai Boulet boulet@uiv-tlse.fr Follow this ad additioal
More informationA sequence of numbers is a function whose domain is the positive integers. We can see that the sequence
Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece,, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet as
More informationSelf-normalized deviation inequalities with application to t-statistic
Self-ormalized deviatio iequalities with applicatio to t-statistic Xiequa Fa Ceter for Applied Mathematics, Tiaji Uiversity, 30007 Tiaji, Chia Abstract Let ξ i i 1 be a sequece of idepedet ad symmetric
More informationBeurling Integers: Part 2
Beurlig Itegers: Part 2 Isomorphisms Devi Platt July 11, 2015 1 Prime Factorizatio Sequeces I the last article we itroduced the Beurlig geeralized itegers, which ca be represeted as a sequece of real umbers
More informationDistance Two Labeling of Some Total Graphs
Gen. Math. Notes, Vol. 3, No. 1, March 2011, pp.100-107 ISSN 2219-7184; Copyright c ICSRS Publication, 2011 www.i-csrs.org Available free online at http://www.geman.in Distance Two Labeling of Some Total
More informationRecursive Algorithm for Generating Partitions of an Integer. 1 Preliminary
Recursive Algorithm for Geeratig Partitios of a Iteger Sug-Hyuk Cha Computer Sciece Departmet, Pace Uiversity 1 Pace Plaza, New York, NY 10038 USA scha@pace.edu Abstract. This article first reviews the
More informationThe Forcing Domination Number of Hamiltonian Cubic Graphs
Iteratioal J.Math. Combi. Vol.2 2009), 53-57 The Forcig Domiatio Number of Hamiltoia Cubic Graphs H.Abdollahzadeh Ahagar Departmet of Mathematics, Uiversity of Mysore, Maasagagotri, Mysore- 570006 Pushpalatha
More information(A sequence also can be thought of as the list of function values attained for a function f :ℵ X, where f (n) = x n for n 1.) x 1 x N +k x N +4 x 3
MATH 337 Sequeces Dr. Neal, WKU Let X be a metric space with distace fuctio d. We shall defie the geeral cocept of sequece ad limit i a metric space, the apply the results i particular to some special
More informationROSE WONG. f(1) f(n) where L the average value of f(n). In this paper, we will examine averages of several different arithmetic functions.
AVERAGE VALUES OF ARITHMETIC FUNCTIONS ROSE WONG Abstract. I this paper, we will preset problems ivolvig average values of arithmetic fuctios. The arithmetic fuctios we discuss are: (1)the umber of represetatios
More informationON THE NUMBER OF LAPLACIAN EIGENVALUES OF TREES SMALLER THAN TWO. Lingling Zhou, Bo Zhou* and Zhibin Du 1. INTRODUCTION
TAIWANESE JOURNAL OF MATHEMATICS Vol 19, No 1, pp 65-75, February 015 DOI: 1011650/tjm190154411 This paper is available olie at http://jouraltaiwamathsocorgtw ON THE NUMBER OF LAPLACIAN EIGENVALUES OF
More informationON BANHATTI AND ZAGREB INDICES
JOURNAL OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4866, ISSN (o) 2303-4947 www.imvibl.org /JOURNALS / JOURNAL Vol. 7(2017), 53-67 DOI: 10.7251/JIMVI1701053G Former BULLETIN OF THE
More informationMAT1026 Calculus II Basic Convergence Tests for Series
MAT026 Calculus II Basic Covergece Tests for Series Egi MERMUT 202.03.08 Dokuz Eylül Uiversity Faculty of Sciece Departmet of Mathematics İzmir/TURKEY Cotets Mootoe Covergece Theorem 2 2 Series of Real
More informationA NEW APPROACH TO SOLVE AN UNBALANCED ASSIGNMENT PROBLEM
A NEW APPROACH TO SOLVE AN UNBALANCED ASSIGNMENT PROBLEM *Kore B. G. Departmet Of Statistics, Balwat College, VITA - 415 311, Dist.: Sagli (M. S.). Idia *Author for Correspodece ABSTRACT I this paper I
More informationLesson 10: Limits and Continuity
www.scimsacademy.com Lesso 10: Limits ad Cotiuity SCIMS Academy 1 Limit of a fuctio The cocept of limit of a fuctio is cetral to all other cocepts i calculus (like cotiuity, derivative, defiite itegrals
More informationThe log-behavior of n p(n) and n p(n)/n
Ramauja J. 44 017, 81-99 The log-behavior of p ad p/ William Y.C. Che 1 ad Ke Y. Zheg 1 Ceter for Applied Mathematics Tiaji Uiversity Tiaji 0007, P. R. Chia Ceter for Combiatorics, LPMC Nakai Uivercity
More information62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +
62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of
More informationThe L(3, 2, 1)-labeling on the Skew and Converse Skew Products of Graphs
Advances in Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 11, Number 1 (2016), pp. 29 36 Research India Publications http://www.ripublication.com/atam.htm The L(3, 2, 1)-labeling on the Skew
More informationMORE GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES
Iraia Joural of Mathematical Scieces ad Iformatics Vol. 2, No. 2 (2007), pp 57-62 MORE GRAPHS WHOSE ENERGY EXCEEDS THE NUMBER OF VERTICES CHANDRASHEKAR ADIGA, ZEYNAB KHOSHBAKHT ad IVAN GUTMAN 1 DEPARTMENT
More informationConfidence interval for the two-parameter exponentiated Gumbel distribution based on record values
Iteratioal Joural of Applied Operatioal Research Vol. 4 No. 1 pp. 61-68 Witer 2014 Joural homepage: www.ijorlu.ir Cofidece iterval for the two-parameter expoetiated Gumbel distributio based o record values
More informationOn Distance and Similarity Measures of Intuitionistic Fuzzy Multi Set
IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578. Volume 5, Issue 4 (Ja. - Feb. 03), PP 9-3 www.iosrourals.org O Distace ad Similarity Measures of Ituitioistic Fuzzy Multi Set *P. Raaraeswari, **N.
More informationAnalytic Continuation
Aalytic Cotiuatio The stadard example of this is give by Example Let h (z) = 1 + z + z 2 + z 3 +... kow to coverge oly for z < 1. I fact h (z) = 1/ (1 z) for such z. Yet H (z) = 1/ (1 z) is defied for
More informationTRACES OF HADAMARD AND KRONECKER PRODUCTS OF MATRICES. 1. Introduction
Math Appl 6 2017, 143 150 DOI: 1013164/ma201709 TRACES OF HADAMARD AND KRONECKER PRODUCTS OF MATRICES PANKAJ KUMAR DAS ad LALIT K VASHISHT Abstract We preset some iequality/equality for traces of Hadamard
More informationA q-analogue of some binomial coefficient identities of Y. Sun
A -aalogue of some biomial coefficiet idetities of Y. Su arxiv:008.469v2 [math.co] 5 Apr 20 Victor J. W. Guo ad Da-Mei Yag 2 Departmet of Mathematics, East Chia Normal Uiversity Shaghai 200062, People
More informationSOME TRIBONACCI IDENTITIES
Mathematics Today Vol.7(Dec-011) 1-9 ISSN 0976-38 Abstract: SOME TRIBONACCI IDENTITIES Shah Devbhadra V. Sir P.T.Sarvajaik College of Sciece, Athwalies, Surat 395001. e-mail : drdvshah@yahoo.com The sequece
More informationAN INTRODUCTION TO SPECTRAL GRAPH THEORY
AN INTRODUCTION TO SPECTRAL GRAPH THEORY JIAQI JIANG Abstract. Spectral graph theory is the study of properties of the Laplacia matrix or adjacecy matrix associated with a graph. I this paper, we focus
More informationON POINTWISE BINOMIAL APPROXIMATION
Iteratioal Joural of Pure ad Applied Mathematics Volume 71 No. 1 2011, 57-66 ON POINTWISE BINOMIAL APPROXIMATION BY w-functions K. Teerapabolar 1, P. Wogkasem 2 Departmet of Mathematics Faculty of Sciece
More informationThe Choquet Integral with Respect to Fuzzy-Valued Set Functions
The Choquet Itegral with Respect to Fuzzy-Valued Set Fuctios Weiwei Zhag Abstract The Choquet itegral with respect to real-valued oadditive set fuctios, such as siged efficiecy measures, has bee used i
More informationk-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c 1. Introduction
Acta Math. Uiv. Comeiaae Vol. LXXXVI, 2 (2017), pp. 279 286 279 k-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c N. IRMAK ad M. ALP Abstract. The k-geeralized Fiboacci sequece { F (k)
More informationA New Solution Method for the Finite-Horizon Discrete-Time EOQ Problem
This is the Pre-Published Versio. A New Solutio Method for the Fiite-Horizo Discrete-Time EOQ Problem Chug-Lu Li Departmet of Logistics The Hog Kog Polytechic Uiversity Hug Hom, Kowloo, Hog Kog Phoe: +852-2766-7410
More informationINEQUALITIES BJORN POONEN
INEQUALITIES BJORN POONEN 1 The AM-GM iequality The most basic arithmetic mea-geometric mea (AM-GM) iequality states simply that if x ad y are oegative real umbers, the (x + y)/2 xy, with equality if ad
More informationON THE LEHMER CONSTANT OF FINITE CYCLIC GROUPS
ON THE LEHMER CONSTANT OF FINITE CYCLIC GROUPS NORBERT KAIBLINGER Abstract. Results of Lid o Lehmer s problem iclude the value of the Lehmer costat of the fiite cyclic group Z/Z, for 5 ad all odd. By complemetary
More informationCOMMON FIXED POINT THEOREMS VIA w-distance
Bulleti of Mathematical Aalysis ad Applicatios ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 3, Pages 182-189 COMMON FIXED POINT THEOREMS VIA w-distance (COMMUNICATED BY DENNY H. LEUNG) SUSHANTA
More informationMA131 - Analysis 1. Workbook 2 Sequences I
MA3 - Aalysis Workbook 2 Sequeces I Autum 203 Cotets 2 Sequeces I 2. Itroductio.............................. 2.2 Icreasig ad Decreasig Sequeces................ 2 2.3 Bouded Sequeces..........................
More informationResearch Article Approximate Riesz Algebra-Valued Derivations
Abstract ad Applied Aalysis Volume 2012, Article ID 240258, 5 pages doi:10.1155/2012/240258 Research Article Approximate Riesz Algebra-Valued Derivatios Faruk Polat Departmet of Mathematics, Faculty of
More informationOscillation and Property B for Third Order Difference Equations with Advanced Arguments
Iter atioal Joural of Pure ad Applied Mathematics Volume 3 No. 0 207, 352 360 ISSN: 3-8080 (prited versio); ISSN: 34-3395 (o-lie versio) url: http://www.ijpam.eu ijpam.eu Oscillatio ad Property B for Third
More informationJoe Holbrook Memorial Math Competition
Joe Holbrook Memorial Math Competitio 8th Grade Solutios October 5, 07. Sice additio ad subtractio come before divisio ad mutiplicatio, 5 5 ( 5 ( 5. Now, sice operatios are performed right to left, ( 5
More informationTHE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES
Joural of Mathematical Aalysis ISSN: 17-341, URL: http://iliriascom/ma Volume 7 Issue 4(16, Pages 13-19 THE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES ABEDALLAH RABABAH, AYMAN AL
More informationFormulas for the Number of Spanning Trees in a Maximal Planar Map
Applied Mathematical Scieces Vol. 5 011 o. 64 3147-3159 Formulas for the Number of Spaig Trees i a Maximal Plaar Map A. Modabish D. Lotfi ad M. El Marraki Departmet of Computer Scieces Faculty of Scieces
More informationBest Optimal Stable Matching
Applied Mathematical Scieces, Vol., 0, o. 7, 7-7 Best Optimal Stable Matchig T. Ramachadra Departmet of Mathematics Govermet Arts College(Autoomous) Karur-6900, Tamiladu, Idia yasrams@gmail.com K. Velusamy
More informationAlternating Series. 1 n 0 2 n n THEOREM 9.14 Alternating Series Test Let a n > 0. The alternating series. 1 n a n.
0_0905.qxd //0 :7 PM Page SECTION 9.5 Alteratig Series Sectio 9.5 Alteratig Series Use the Alteratig Series Test to determie whether a ifiite series coverges. Use the Alteratig Series Remaider to approximate
More informationOn Edge Regular Fuzzy Line Graphs
Iteratioal Joural of Computatioal ad Applied Mathematics ISSN 1819-4966 Volume 11, Number 2 (2016), pp 105-118 Research Idia Publicatios http://wwwripublicatiocom O Edge Regular Fuzz Lie Graphs K Radha
More informationAxioms of Measure Theory
MATH 532 Axioms of Measure Theory Dr. Neal, WKU I. The Space Throughout the course, we shall let X deote a geeric o-empty set. I geeral, we shall ot assume that ay algebraic structure exists o X so that
More informationSquare-Congruence Modulo n
Square-Cogruece Modulo Abstract This paper is a ivestigatio of a equivalece relatio o the itegers that was itroduced as a exercise i our Discrete Math class. Part I - Itro Defiitio Two itegers are Square-Cogruet
More informationON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS
Joural of Algebra, Number Theory: Advaces ad Applicatios Volume, Number, 00, Pages 7-89 ON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS OLCAY KARAATLI ad REFİK KESKİN Departmet
More informationSome Oscillation Properties of Third Order Linear Neutral Delay Difference Equations
ISSN (e): 50 3005 Volume, 05 Issue, 07 July 05 Iteratioal Joural of Computatioal Egieerig Research (IJCER) Some Oscillatio Properties of Third Order Liear Neutral Delay Differece Equatios AGeorge Maria
More informationONE MODULO THREE GEOMETRIC MEAN LABELING OF SOME FAMILIES OF GRAPHS
ONE MODULO THREE GEOMETRIC MEAN LABELING OF SOME FAMILIES OF GRAPHS A.Maheswari 1, P.Padiaraj 2 1,2 Departet of Matheatics,Kaaraj College of Egieerig ad Techology, Virudhuagar (Idia) ABSTRACT A graph G
More informationInfinite Sequences and Series
Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet
More informationLecture 2 Clustering Part II
COMS 4995: Usupervised Learig (Summer 8) May 24, 208 Lecture 2 Clusterig Part II Istructor: Nakul Verma Scribes: Jie Li, Yadi Rozov Today, we will be talkig about the hardess results for k-meas. More specifically,
More informationJournal of Ramanujan Mathematical Society, Vol. 24, No. 2 (2009)
Joural of Ramaua Mathematical Society, Vol. 4, No. (009) 199-09. IWASAWA λ-invariants AND Γ-TRANSFORMS Aupam Saikia 1 ad Rupam Barma Abstract. I this paper we study a relatio betwee the λ-ivariats of a
More informationsubcaptionfont+=small,labelformat=parens,labelsep=space,skip=6pt,list=0,hypcap=0 subcaption ALGEBRAIC COMBINATORICS LECTURE 8 TUESDAY, 2/16/2016
subcaptiofot+=small,labelformat=pares,labelsep=space,skip=6pt,list=0,hypcap=0 subcaptio ALGEBRAIC COMBINATORICS LECTURE 8 TUESDAY, /6/06. Self-cojugate Partitios Recall that, give a partitio λ, we may
More informationSome Common Fixed Point Theorems in Cone Rectangular Metric Space under T Kannan and T Reich Contractive Conditions
ISSN(Olie): 319-8753 ISSN (Prit): 347-671 Iteratioal Joural of Iovative Research i Sciece, Egieerig ad Techology (A ISO 397: 7 Certified Orgaizatio) Some Commo Fixed Poit Theorems i Coe Rectagular Metric
More informationOn Net-Regular Signed Graphs
Iteratioal J.Math. Combi. Vol.1(2016), 57-64 O Net-Regular Siged Graphs Nuta G.Nayak Departmet of Mathematics ad Statistics S. S. Dempo College of Commerce ad Ecoomics, Goa, Idia E-mail: ayakuta@yahoo.com
More informationMi-Hwa Ko and Tae-Sung Kim
J. Korea Math. Soc. 42 2005), No. 5, pp. 949 957 ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY ORTHANT DEPENDENT RANDOM VARIABLES Mi-Hwa Ko ad Tae-Sug Kim Abstract. For weighted sum of a sequece
More informationA class of spectral bounds for Max k-cut
A class of spectral bouds for Max k-cut Miguel F. Ajos, José Neto December 07 Abstract Let G be a udirected ad edge-weighted simple graph. I this paper we itroduce a class of bouds for the maximum k-cut
More informationFans are cycle-antimagic
AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 68(1 (017, Pages 94 105 Fas are cycle-atimagic Ali Ovais Muhammad Awais Umar Abdus Salam School of Mathematical Scieces GC Uiversity, Lahore Pakista aligureja
More informationInternational Journal of Mathematical Archive-3(4), 2012, Page: Available online through ISSN
Iteratioal Joural of Mathematical Archive-3(4,, Page: 544-553 Available olie through www.ima.ifo ISSN 9 546 INEQUALITIES CONCERNING THE B-OPERATORS N. A. Rather, S. H. Ahager ad M. A. Shah* P. G. Departmet
More informationAPPROXIMATE FUNCTIONAL INEQUALITIES BY ADDITIVE MAPPINGS
Joural of Mathematical Iequalities Volume 6, Number 3 0, 46 47 doi:0.753/jmi-06-43 APPROXIMATE FUNCTIONAL INEQUALITIES BY ADDITIVE MAPPINGS HARK-MAHN KIM, JURI LEE AND EUNYOUNG SON Commuicated by J. Pečarić
More information