Square Difference Labeling Of Some Path, Fan and Gear Graphs
|
|
- Julian Oliver
- 5 years ago
- Views:
Transcription
1 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 ISSN Square Dfferece Labelg Of Some Path, Fa ad Gear Graphs J.Shama Assstat Professor Departmet of Mathematcs CMS College of Scece ad Commerce Combatore , Taml Nadu, Ida Emal: Abstract: I ths paper t s proved that some ew graphs admt square dfferece labelg. A fucto f s called a square dfferece labelg f there exst a bjecto f: V(G) {0,,,.p-} such that the duced fucto f * :E(G) N gve by f * (u v) = [f(u)] - [f(v)] for every uv E(G) are all dstct. Ay graphs whch satsfes the Square dfferece labelg s called the Square dfferece graph. Here t s vestgated that the cetral graphs of path, square graphs of path, some path related graphs, fa ad gear graphs are all square dfferece graphs. Keywords: Square dfferece labelg, square dfferece graphs, cetral graphs ad power graphs.. INTRODUTION All graphs ths paper are fte ad udrected. For all other termology ad otatos I follow Harary [ ].Let G (V,E) be a graph where the symbols V (G) ad E (G) deotes the vertex set ad the edge set. The cardalty of the vertex set s called the order of the graph G ad t s deoted by p. The cardalty of the edge set s called the sze of the graph G ad t s deoted by q. Hece the graph s deoted by G (p, q).if the vertces of the graph are assged values subject to certa codtos s kow as graph labelg. The deftos for power graphs are used from Gary Chatrad [4].Some basc cocepts are take from [5] ad [] A dyamc survey o graph labelg s regularly updated by Galla [3] ad t s publshed by Electroc Joural of Combatorcs. The square sum labelg s prevously defed by V.Ajtha, S.Arumugam ad K.A.Germa []. I proved some mddle ad total graphs [6] are square sum graphs. The cocept of square dfferece labelg was frst troduced by J.Shama [9]. Myself proved [9] ad [0] may stadard graphs lke P, C, complete graphs, cycle cactus, ladder, lattce grds, quadrlateral sakes, Wheels, K+ m K, comb, star graphs, m K3, m C3,duplcato of vertces by a edge to some star graphs ad crow graphs are square dfferece graphs. Also proved that the path s a odd square dfferece graphs ad star graphs are perfect square graphs. Some IJSER 03
2 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 ISSN graphs lke shadow ad splt graphs [7], [8] ca also be vestgated for the square dfferece labelg. Result-: Path graphs are square dfferece graphs [0] Result-: Wheels graphs are square dfferece graphs [9]. MAIN RESULTS Defto.: Let G = (V(G),E(G)) be a graph.a fucto f s called a square dfferece labelg f there exst a bjecto f: V(G) {0,,,.p-} such that the duced fucto f * :E(G) N gve by f * (u v) = [f(u)] - [f(v)] for every uv E(G) are all dstct. Defto.: Ay graph whch admts square dfferece labelg s called square dfferece graph. Defto.3:The k th power G k of a coected graph G,where k, s that graph wth V(G k ) = V(G) for whch uv E(G k ) f ad oly f dg (u,v) k.the graphs G ad G 3 are also referred to as square ad cube respectvely of G. Defto.4: Let G be a fte udrected graph wth o loops ad multple edges. The cetral graph C(G) of a graph G s obtaed by subdvdg each edge of G exactly oce ad jog all the o adjacet vertces of G. By defto vertces of the cetral graph s Pc(G) = p + q, where p ad q are umber of vertces ad edges G. For ay graph (p,q) there exsts p vertces of degree p- ad q vertces of degree C(G) Defto.5: The graph (P; K ) s obtaed from a path P by jog a pedat edge at each vertex of the path. Defto.6: Let Sm be a star graph wth vertces v, w, w,..., wm. Defe (P; Sm ) the graph obtaed from m copes of Sm ad the path P: u, u,..., u by jog uj wth the vertex v of the j th copy of Sm by meas of a edge, m 3, j. Theorem-.7: Cetral graph of a path P admts square dfferece labelg Proof: Let P : u, u,, u. Sub dvde the edges by v, v,, v-. Let G = C(P) p = V (G) = - (+)/ ad q = E (G) = (-) Defe f: V (G) {0,,,.p-} as follows f(u) = -, - f(v) = -, - We costruct the vertex labeled sets as follows. V = { f ( )} u = { } = {0,,4,,, -} V = { f ( )} v = { j } = {, 3, 5,, -3} We costruct the edge labeled sets as follows. { * E = f ( u v )} = { ( ) ( ) IJSER 03
3 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 3 ISSN = = { 4 3 {4 3} = {,5,9,...,4-7} { E = f *( v u )} = { [ f ( v )] [ f ( u )] = {( ) () = { [ f ( u )] [ f ( u )] 3 = {( ) ( 4) = { 4 = { 36, 60,...,4+} All the edges all the sets are dstct. Hece the cetral graphs of path admt square dfferece labelg. Example-.8: Cetral graph of a path P4 admts square dfferece labelg = = { 4 {4 } = {3,7,,...,4-5} { E3 = f *( u u )} = { [ f ( u )] [ f ( u )] = {( ) ( ) {6 = } ={ 6,3,... } { 3 E4 = f *( u u )} 3. Some path related graphs Theorem- 3.: The graph P s a square dfferece graph. Proof: Let P: u, u,..., u be a path. Let G = P p = V (G) = ad q = E (G) = -3. Defe a vertex labelg f: V (G) {0,,,...p-} by f(u) = -, ad the duced edge labelg fucto f * : E (G) N defed by f * (u v) = [f(u)] - [f(v)] for every uv E(G) are all dstct. such that f * (e) f * (ej) for every e ej IJSER 03
4 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 4 ISSN E = {(uu+) / -} E = {(uu+) / -} I E f * (u u+) = { [ f ( u )] [ f ( u )] I E = {( ) = { ={,3,5,... -3} f * (u u+) = { [ f ( u )] [ f ( u )] = { ( ) ( ) = { 4 ={4,8,,... 4(-)} Clearly the labelg of edges of E ad that of E are all dstct, as E cotas odd umbers ad E cotas eve umbers.therefore P are square dfferece graphs. Example 3.: The graph P6 s a square dfferece graph Proof: Let G = (P, K ), V (G) = ad E (G) = -. Defe the vertex labelg f: V (G) {0,,,.p-} by f(u) = -, f(v) = + -, ad the duced edge labelg fucto f * : E (G) N defed by f * (u v) = [f(u)] - [f(v)] for every uv E(G) are all dstct. such that f * (e) f * (ej) for every e ej E = {(uu+) / -} E = {(uv) / } I E f * (u u+) = { [ f ( u )] [ f ( u )] = {( ( ) = {( ( ) ={,3,5,... -3} I E f * (u v) = { [ f ( u )] [ f ( v )] Theorem- 3.3: The graph (P, K ) s a square dfferece graph = {( ( ) ( ) IJSER 03
5 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 5 ISSN = {( (( ) ={,+,4+, } Clearly the edge labels are dstct. Hece the graphs (P, K ) admt the square dfferece labelg. Example 3.4: The graph (P, K ) s a square dfferece graph E = {(uv) / } E3 = {(vw) / } I E f * (u u + ) = { [ f ( u )] [ f ( u )] = {( ) ( ) = {( ) ={,3,5,... -3} I E Theorem- 3.5: The graph (P, S ) s a square dfferece graph Proof: Let G = (P, S ), V (G) = 3 ad E (G) = 3-. Defe the vertex labelg f: V (G) {0,,,.p-} by f(u) = -, f(v) = +-, f(w) = + -, ad the duced edge labelg fucto f * : E (G) N defed by f * (u v) = [f(u)] - [f(v)] for every uv E(G) are all dstct. such that f * (e) f * (ej) for every e ej E = {(uu+) / -} f * (u v ) = { [ f ( u )] [ f ( v )] I E3 = {( ( ) ( ) = {( ( ={,+,4+, } f * (v w) = { [ f ( v )] [ f ( w )] = { ( ) ( ) = {( ( 3 ={3,+3,4+3, } Clearly the edge labels are dstct. Hece the graphs (P, S ) are square dfferece graphs. IJSER 03
6 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 6 ISSN Example 3.6: The graph (P4, S ) s a square dfferece graph = {( ( ) = {( ={,3,5,... -3} Theorem- 3.7: The graph (P, S ) s a square dfferece graph Proof: Let G = (P, S ), V (G) = 4 ad E (G) = 4-. Defe the vertex labelg f: V (G) {0,,,.p-} by f(u) = -, f(v) = - +, f(w) =- +, ad the duced edge labelg fucto f * : E (G) N defed by f * (u v) = [f(u)] - [f(v)] for every uv E(G) are all dstct. such that f * (e) f * (ej) for every e ej E = {(uu+) / -} E = {(uv) / } E3 = {(vw -) / } E4 = {(vw ) / } I E f * (u v) = { [ f ( u )] [ f ( v )] I E3 = {( ( ) ( ) = {( ( ={,+,4+, } f * (v w-) = { [ f ( v )] [ f ( w )] I E4 = { ( ) ( ) = {( 3( = {3, 3(+),..., 3(-) } f * (v w) = { [ f ( v )] [ f ( w )] I E f * (u u+) = { [ f ( u )] [ f ( u )] = { ( ) ( ) = {( ( IJSER 03
7 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 7 ISSN = {( 3( ) ( All the edge labels E, E, E3 ad E4 are all dstct. Hece the graphs (P, S ) are square dfferece graphs. Example 3.8: The graph (P4, S ) s a square dfferece graph ad the duced edge labelg fucto f * : E (G) N by f * (u v) = [f(u)] - [f(v)] for every uv E(G) are all dstct. E = {(uu+) / -} E = {(cu) / } The vertex sets are V= f(c) = 0 V f ( u ) Theorem- 3.9: The graph (P, S3 ) s a square dfferece graph Proof9 Example 3.0: The graph (P4, S3 ) s a square dfferece graph ( ) = {,,...,-} I E * E = { f ( cu )} { [ f ( c)] [ f ( u )] 4. Some other graphs Theorem- 4.: Fa graphs are square dfferece graphs. Proof: Let F be a fa wth vertces u,u,u,...,u. Let G = F, V (G) = + ad E (G) = 3. Defe the vertex labelg f: V (G) {0,,,.p-} by f(u) =, ad f(c) = 0 0 ( ) ( ) = {,9,5,...,(-) } I E {,3 E = f * ( u u )},,3 { [ f ( u )] [ f ( u )] IJSER 03
8 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 8 ISSN = { ( ) ( ),3 =,3 { ={3,7,,...,4-} clearly the edge labels are dstct. Hece the Fas are all square dfferece graphs. Example 4.: The fa graph F5 s a square dfferece graph E = {(uv) / } E = {(vu+) / } E3 = {(uu) / } I E f * (u v) = { [ f ( u )] [ f ( v )] = {( ) ( ) = {( ( ={48,60,7,... 3 } I E f * (v u+) = { [ f ( v )] [ f ( u )] Theorem- 4.3: Gear graphs G are square dfferece graphs. Proof: Let V (G) = + ad E (G) = 3. Let us defe the vertex labelg f: V (G) {0,,,.p-} as follows f(u) = 0 f(u) =, = {( ) ( ) = {( ) = {45, 55,... } * E3 = { f ( u u )} f(v) = +, Ad the duced edge labelg fucto { [ f ( u )] [ f ( u )] f * : E (G) N defed by f * (u v) = [f(u)] - [f(v)] for every uv E(G) are all dstct. such that f * (e) f * (ej) for every e ej = { (0) ( ) =, { IJSER 03
9 Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 9 ISSN ={,4,,..., } I E4 * E4 = { f ( u v )} { [ f ( u )] [ f ( v = { () ={4 -} All the edges are dstct. Hece all the gear graphs G are square dfferece graphs. Example 4.4: The gear graph G6 s a square dfferece graph )] [] Frak Harary, Graph theory, Narosa Publshg House- (00). [3] J A Galla, A dyamc survey of graph labelg, The Electrocs joural of Combatores, 7(00) # DS6 [4]Gary Chartrad, ad Lesak, Graphs ad dgraphs, fourth edto, Chapma & HALL/CRC [5]Gary Chartrad, Pg Zhag, Itroducto to Graph theory, McGraw- Hll Iteratoal Edto [6] J.Shama Square sum labelg for some mddle ad total graphs Iteratoal Joural of Computer Applcatos ( ) Volume 37- No.4 Jauary 0 [7] J.Shama Square dfferece labelg for some graphs Iteratoal Joural of Computer Applcatos ( ) Volume 44- No.4, Aprl 0 [8] J.Shama Some Specal types of Square dfferece graphs Iteratoal Joural of Mathematcal archves- 3(6),0, ISSN [9]D B West, Itroducto to Graph Theory, Pretce-Hall, Ida, 00 Cocluso: I ths paper t s proved that some path graphs admts square dfferece labelg. Also proved some fa ad gear graphs admt square dfferece labelg. I my prevous papers [7],[8] t s proved that some graphs are square dfferece graphs. The square dfferece labelg ca be vestgated for more graphs. It s a ope problem. REFERENCES []V.Ajtha, S.Arumugam ad K.A.Germa O Square sum graphs AKCE J.Graphs, Comb, 6(006) - 0 IJSER 03
V. Hemalatha, V. Mohana Selvi,
Iteratoal Joural of Scetfc & Egeerg Research, Volue 6, Issue, Noveber-0 ISSN - SUPER GEOMETRIC MEAN LABELING OF SOME CYCLE RELATED GRAPHS V Healatha, V Mohaa Selv, ABSTRACT-Let G be a graph wth p vertces
More informationFurther Results on Pair Sum Labeling of Trees
Appled Mathematcs 0 70-7 do:046/am0077 Publshed Ole October 0 (http://wwwscrporg/joural/am) Further Results o Par Sum Labelg of Trees Abstract Raja Poraj Jeyaraj Vjaya Xaver Parthpa Departmet of Mathematcs
More information1 Edge Magic Labeling for Special Class of Graphs
S.Srram et. al. / Iteratoal Joural of Moder Sceces ad Egeerg Techology (IJMSET) ISSN 349-3755; Avalable at https://www.jmset.com Volume, Issue 0, 05, pp.60-67 Edge Magc Labelg for Specal Class of Graphs
More informationSUPER GRACEFUL LABELING FOR SOME SPECIAL GRAPHS
IJRRAS 9 ) Deceber 0 www.arpapress.co/volues/vol9issue/ijrras_9 06.pdf SUPER GRACEFUL LABELING FOR SOME SPECIAL GRAPHS M.A. Perual, S. Navaeethakrsha, S. Arockara & A. Nagaraa 4 Departet of Matheatcs,
More informationMean Cordial Labeling of Certain Graphs
J Comp & Math Sc Vol4 (4), 74-8 (03) Mea Cordal Labelg o Certa Graphs ALBERT WILLIAM, INDRA RAJASINGH ad S ROY Departmet o Mathematcs, Loyola College, Chea, INDIA School o Advaced Sceces, VIT Uversty,
More informationK-Even Edge-Graceful Labeling of Some Cycle Related Graphs
Iteratoal Joural of Egeerg Scece Iveto ISSN (Ole): 9 7, ISSN (Prt): 9 7 www.jes.org Volume Issue 0ǁ October. 0 ǁ PP.0-7 K-Eve Edge-Graceful Labelg of Some Cycle Related Grahs Dr. B. Gayathr, S. Kousalya
More informationOn Face Bimagic Labeling of Graphs
IOSR Joural of Mathematcs (IOSR-JM) e-issn: 78-578, p-issn: 319-765X Volume 1, Issue 6 Ver VI (Nov - Dec016), PP 01-07 wwwosrouralsor O Face Bmac Label of Graphs Mohammed Al Ahmed 1,, J Baskar Babuee 1
More informationOn Signed Product Cordial Labeling
Appled Mathematcs 55-53 do:.436/am..6 Publshed Ole December (http://www.scrp.or/joural/am) O Sed Product Cordal Label Abstract Jayapal Baskar Babujee Shobaa Loaatha Departmet o Mathematcs Aa Uversty Chea
More informationOn Complementary Edge Magic Labeling of Certain Graphs
Amerca Joural of Mathematcs ad Statstcs 0, (3: -6 DOI: 0.593/j.ajms.0003.0 O Complemetary Edge Magc Labelg of Certa Graphs Sajay Roy,*, D.G. Akka Research Scholar, Ida Academc Dea, HMS sttute of Techology,
More informationDouble Dominating Energy of Some Graphs
Iter. J. Fuzzy Mathematcal Archve Vol. 4, No., 04, -7 ISSN: 30 34 (P), 30 350 (ole) Publshed o 5 March 04 www.researchmathsc.org Iteratoal Joural of V.Kaladev ad G.Sharmla Dev P.G & Research Departmet
More informationOn Eccentricity Sum Eigenvalue and Eccentricity Sum Energy of a Graph
Aals of Pure ad Appled Mathematcs Vol. 3, No., 7, -3 ISSN: 79-87X (P, 79-888(ole Publshed o 3 March 7 www.researchmathsc.org DOI: http://dx.do.org/.7/apam.3a Aals of O Eccetrcty Sum Egealue ad Eccetrcty
More information(k,d) Mean Labeling of Some Family of Trees
Iteratoal Joral of Scece ad Research (IJSR) ISSN (Ole): -0 Idex Copercs Vale (0):. Impact Factor (0):. (k,d)mea Labelg of Some Famly of Trees B. Gayathr, V. Slochaa PG ad Research Departmet of Mathematcs,
More informationNon-uniform Turán-type problems
Joural of Combatoral Theory, Seres A 111 2005 106 110 wwwelsevercomlocatecta No-uform Turá-type problems DhruvMubay 1, Y Zhao 2 Departmet of Mathematcs, Statstcs, ad Computer Scece, Uversty of Illos at
More informationBounds for the Connective Eccentric Index
It. J. Cotemp. Math. Sceces, Vol. 7, 0, o. 44, 6-66 Bouds for the Coectve Eccetrc Idex Nlaja De Departmet of Basc Scece, Humates ad Socal Scece (Mathematcs Calcutta Isttute of Egeerg ad Maagemet Kolkata,
More informationA Study on Generalized Generalized Quasi hyperbolic Kac Moody algebra QHGGH of rank 10
Global Joural of Mathematcal Sceces: Theory ad Practcal. ISSN 974-3 Volume 9, Number 3 (7), pp. 43-4 Iteratoal Research Publcato House http://www.rphouse.com A Study o Geeralzed Geeralzed Quas (9) hyperbolc
More informationLebesgue Measure of Generalized Cantor Set
Aals of Pure ad Appled Mathematcs Vol., No.,, -8 ISSN: -8X P), -888ole) Publshed o 8 May www.researchmathsc.org Aals of Lebesgue Measure of Geeralzed ator Set Md. Jahurul Islam ad Md. Shahdul Islam Departmet
More informationPROJECTION PROBLEM FOR REGULAR POLYGONS
Joural of Mathematcal Sceces: Advaces ad Applcatos Volume, Number, 008, Pages 95-50 PROJECTION PROBLEM FOR REGULAR POLYGONS College of Scece Bejg Forestry Uversty Bejg 0008 P. R. Cha e-mal: sl@bjfu.edu.c
More informationUniform asymptotical stability of almost periodic solution of a discrete multispecies Lotka-Volterra competition system
Iteratoal Joural of Egeerg ad Advaced Research Techology (IJEART) ISSN: 2454-9290, Volume-2, Issue-1, Jauary 2016 Uform asymptotcal stablty of almost perodc soluto of a dscrete multspeces Lotka-Volterra
More informationResearch Article A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings
Hdaw Publshg Corporato Iteratoal Joural of Mathematcs ad Mathematcal Sceces Volume 009, Artcle ID 391839, 9 pages do:10.1155/009/391839 Research Artcle A New Iteratve Method for Commo Fxed Pots of a Fte
More informationPAijpam.eu SOME NEW SUM PERFECT SQUARE GRAPHS S.G. Sonchhatra 1, G.V. Ghodasara 2
Internatonal Journal of Pure and Appled Mathematcs Volume 113 No. 3 2017, 489-499 ISSN: 1311-8080 (prnted verson); ISSN: 1314-3395 (on-lne verson) url: http://www.jpam.eu do: 10.12732/jpam.v1133.11 PAjpam.eu
More informationOn Submanifolds of an Almost r-paracontact Riemannian Manifold Endowed with a Quarter Symmetric Metric Connection
Theoretcal Mathematcs & Applcatos vol. 4 o. 4 04-7 ISS: 79-9687 prt 79-9709 ole Scepress Ltd 04 O Submafolds of a Almost r-paracotact emaa Mafold Edowed wth a Quarter Symmetrc Metrc Coecto Mob Ahmad Abdullah.
More informationSome identities involving the partial sum of q-binomial coefficients
Some dettes volvg the partal sum of -bomal coeffcets Bg He Departmet of Mathematcs, Shagha Key Laboratory of PMMP East Cha Normal Uversty 500 Dogchua Road, Shagha 20024, People s Republc of Cha yuhe00@foxmal.com
More informationAnalysis of Lagrange Interpolation Formula
P IJISET - Iteratoal Joural of Iovatve Scece, Egeerg & Techology, Vol. Issue, December 4. www.jset.com ISS 348 7968 Aalyss of Lagrage Iterpolato Formula Vjay Dahya PDepartmet of MathematcsMaharaja Surajmal
More informationBivariate Vieta-Fibonacci and Bivariate Vieta-Lucas Polynomials
IOSR Joural of Mathematcs (IOSR-JM) e-issn: 78-78, p-issn: 19-76X. Volume 1, Issue Ver. II (Jul. - Aug.016), PP -0 www.osrjourals.org Bvarate Veta-Fboacc ad Bvarate Veta-Lucas Polomals E. Gokce KOCER 1
More informationExpanding Super Edge-Magic Graphs
PROC. ITB Sas & Tek. Vol. 36 A, No., 00, 7-5 7 Exadg Suer Edge-Magc Grahs E. T. Baskoro & Y. M. Cholly, Deartet of Matheatcs, Isttut Tekolog Badug Jl. Gaesa 0 Badug 03, Idoesa Eals : {ebaskoro,yus}@ds.ath.tb.ac.d
More informationHarmonic Mean Labeling for Some Special Graphs
International Journal of Mathematics Research. ISSN 0976-5840 Volume 5, Number 1 (2013), pp. 55-64 International Research Publication House http://www.irphouse.com Harmonic Mean Labeling for Some Special
More informationρ < 1 be five real numbers. The
Lecture o BST 63: Statstcal Theory I Ku Zhag, /0/006 Revew for the prevous lecture Deftos: covarace, correlato Examples: How to calculate covarace ad correlato Theorems: propertes of correlato ad covarace
More informationThe Mathematical Appendix
The Mathematcal Appedx Defto A: If ( Λ, Ω, where ( λ λ λ whch the probablty dstrbutos,,..., Defto A. uppose that ( Λ,,..., s a expermet type, the σ-algebra o λ λ λ are defed s deoted by ( (,,...,, σ Ω.
More informationPacking of graphs with small product of sizes
Joural of Combatoral Theory, Seres B 98 (008) 4 45 www.elsever.com/locate/jctb Note Packg of graphs wth small product of szes Alexadr V. Kostochka a,b,,gexyu c, a Departmet of Mathematcs, Uversty of Illos,
More informationQ-analogue of a Linear Transformation Preserving Log-concavity
Iteratoal Joural of Algebra, Vol. 1, 2007, o. 2, 87-94 Q-aalogue of a Lear Trasformato Preservg Log-cocavty Daozhog Luo Departmet of Mathematcs, Huaqao Uversty Quazhou, Fua 362021, P. R. Cha ldzblue@163.com
More informationMAX-MIN AND MIN-MAX VALUES OF VARIOUS MEASURES OF FUZZY DIVERGENCE
merca Jr of Mathematcs ad Sceces Vol, No,(Jauary 0) Copyrght Md Reader Publcatos wwwjouralshubcom MX-MIN ND MIN-MX VLUES OF VRIOUS MESURES OF FUZZY DIVERGENCE RKTul Departmet of Mathematcs SSM College
More informationNP!= P. By Liu Ran. Table of Contents. The P versus NP problem is a major unsolved problem in computer
NP!= P By Lu Ra Table of Cotets. Itroduce 2. Prelmary theorem 3. Proof 4. Expla 5. Cocluso. Itroduce The P versus NP problem s a major usolved problem computer scece. Iformally, t asks whether a computer
More informationX ε ) = 0, or equivalently, lim
Revew for the prevous lecture Cocepts: order statstcs Theorems: Dstrbutos of order statstcs Examples: How to get the dstrbuto of order statstcs Chapter 5 Propertes of a Radom Sample Secto 55 Covergece
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 informationA New Method for Solving Fuzzy Linear. Programming by Solving Linear Programming
ppled Matheatcal Sceces Vol 008 o 50 7-80 New Method for Solvg Fuzzy Lear Prograg by Solvg Lear Prograg S H Nasser a Departet of Matheatcs Faculty of Basc Sceces Mazadara Uversty Babolsar Ira b The Research
More informationNP!= P. By Liu Ran. Table of Contents. The P vs. NP problem is a major unsolved problem in computer
NP!= P By Lu Ra Table of Cotets. Itroduce 2. Strategy 3. Prelmary theorem 4. Proof 5. Expla 6. Cocluso. Itroduce The P vs. NP problem s a major usolved problem computer scece. Iformally, t asks whether
More informationSolving Constrained Flow-Shop Scheduling. Problems with Three Machines
It J Cotemp Math Sceces, Vol 5, 2010, o 19, 921-929 Solvg Costraed Flow-Shop Schedulg Problems wth Three Maches P Pada ad P Rajedra Departmet of Mathematcs, School of Advaced Sceces, VIT Uversty, Vellore-632
More informationA Remark on the Uniform Convergence of Some Sequences of Functions
Advaces Pure Mathematcs 05 5 57-533 Publshed Ole July 05 ScRes. http://www.scrp.org/joural/apm http://dx.do.org/0.436/apm.05.59048 A Remark o the Uform Covergece of Some Sequeces of Fuctos Guy Degla Isttut
More informationGeneralization of the Dissimilarity Measure of Fuzzy Sets
Iteratoal Mathematcal Forum 2 2007 o. 68 3395-3400 Geeralzato of the Dssmlarty Measure of Fuzzy Sets Faramarz Faghh Boformatcs Laboratory Naobotechology Research Ceter vesa Research Isttute CECR Tehra
More informationOn L- Fuzzy Sets. T. Rama Rao, Ch. Prabhakara Rao, Dawit Solomon And Derso Abeje.
Iteratoal Joural of Fuzzy Mathematcs ad Systems. ISSN 2248-9940 Volume 3, Number 5 (2013), pp. 375-379 Research Ida Publcatos http://www.rpublcato.com O L- Fuzzy Sets T. Rama Rao, Ch. Prabhakara Rao, Dawt
More informationLecture 12 APPROXIMATION OF FIRST ORDER DERIVATIVES
FDM: Appromato of Frst Order Dervatves Lecture APPROXIMATION OF FIRST ORDER DERIVATIVES. INTRODUCTION Covectve term coservato equatos volve frst order dervatves. The smplest possble approach for dscretzato
More informationTotal Prime Graph. Abstract: We introduce a new type of labeling known as Total Prime Labeling. Graphs which admit a Total Prime labeling are
Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu. 5 Total Prm Graph M.Rav (a) Ramasubramaa 1, R.Kala 1 Dpt.of Mathmatcs, Sr Shakth Isttut of Egrg & Tchology, Combator 641 06. Dpt. of Mathmatcs,
More informationEstimation of Stress- Strength Reliability model using finite mixture of exponential distributions
Iteratoal Joural of Computatoal Egeerg Research Vol, 0 Issue, Estmato of Stress- Stregth Relablty model usg fte mxture of expoetal dstrbutos K.Sadhya, T.S.Umamaheswar Departmet of Mathematcs, Lal Bhadur
More informationChapter 5 Properties of a Random Sample
Lecture 6 o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for the prevous lecture Cocepts: t-dstrbuto, F-dstrbuto Theorems: Dstrbutos of sample mea ad sample varace, relatoshp betwee sample mea ad sample
More informationJournal of Mathematical Analysis and Applications
J. Math. Aal. Appl. 365 200) 358 362 Cotets lsts avalable at SceceDrect Joural of Mathematcal Aalyss ad Applcatos www.elsever.com/locate/maa Asymptotc behavor of termedate pots the dfferetal mea value
More informationConnective Eccentricity Index of Some Thorny Graphs
Aals of ure ad Appled Matheatcs Vol. 7, No., 04, 59-64 IN: 79-087X (), 79-0888(ole) ublshed o 9 epteber 04 www.researchathsc.org Aals of oectve Eccetrcty Idex of oe Thory raphs Nlaja De, k. Md. Abu Nayee
More informationmeans the first term, a2 means the term, etc. Infinite Sequences: follow the same pattern forever.
9.4 Sequeces ad Seres Pre Calculus 9.4 SEQUENCES AND SERIES Learg Targets:. Wrte the terms of a explctly defed sequece.. Wrte the terms of a recursvely defed sequece. 3. Determe whether a sequece s arthmetc,
More informationVertex Graceful Labeling-Some Path Related Graphs
Internatonal J.Math. Combn. Vol.3013), 44-49 Vertex Graceful Labelng-Some Path Related Graphs P.Selvaraju 1, P.Balaganesan and J.Renuka 3 1 Department of Mathematcs, Vel Tech Engneerng College, Avad, Chenna-
More informationInternational Journal of Advancements in Research & Technology, Volume 3, Issue 9, September ISSN
Iteratoal Joural of dvacemets Research & Techology, Volume 3, Issue 9, September -2014 8 Topologcal Propertes o Measure space(r, T wth Measure codto S. C. P. Halakatt 1 ad H. G. Halol 2 1 Departmet of
More informationTopological Indices of Hypercubes
202, TextRoad Publcato ISSN 2090-4304 Joural of Basc ad Appled Scetfc Research wwwtextroadcom Topologcal Idces of Hypercubes Sahad Daeshvar, okha Izbrak 2, Mozhga Masour Kalebar 3,2 Departmet of Idustral
More information1 Onto functions and bijections Applications to Counting
1 Oto fuctos ad bectos Applcatos to Coutg Now we move o to a ew topc. Defto 1.1 (Surecto. A fucto f : A B s sad to be surectve or oto f for each b B there s some a A so that f(a B. What are examples of
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 Primitive Idempotents in
Iteratoal Joural of Algebra, Vol, 00, o 5, 3 - The Prmtve Idempotets FC - I Kulvr gh Departmet of Mathematcs, H College r Jwa Nagar (rsa)-5075, Ida kulvrsheora@yahoocom K Arora Departmet of Mathematcs,
More informationSome distances and sequences in a weighted graph
IOSR Joural of Mathematc (IOSR-JM) e-issn: 78-578 p-issn: 19 765X PP 7-15 wwworjouralorg Some dtace ad equece a weghted graph Jll K Mathew 1, Sul Mathew Departmet of Mathematc Federal Ittute of Scece ad
More informationAn Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc. Research on scheme evaluation method of automation mechatronic systems
[ype text] [ype text] [ype text] ISSN : 0974-7435 Volume 0 Issue 6 Boechology 204 Ida Joural FULL PPER BIJ, 0(6, 204 [927-9275] Research o scheme evaluato method of automato mechatroc systems BSRC Che
More informationSQUARE DIFFERENCE 3-EQUITABLE LABELING FOR SOME GRAPHS. Sattur , TN, India. Sattur , TN, India.
International Journal of Science, Engineering Technology Research (IJSETR), Volume 5, Issue, March 2016 SQUARE DIFFERENCE -EQUITABLE LABELING FOR SOME GRAPHS R Loheswari 1 S Saravana kumar 2 1 Research
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 informationAbout k-perfect numbers
DOI: 0.47/auom-04-0005 A. Şt. Uv. Ovdus Costaţa Vol.,04, 45 50 About k-perfect umbers Mhály Becze Abstract ABSTRACT. I ths paper we preset some results about k-perfect umbers, ad geeralze two equaltes
More informationCHAPTER VI Statistical Analysis of Experimental Data
Chapter VI Statstcal Aalyss of Expermetal Data CHAPTER VI Statstcal Aalyss of Expermetal Data Measuremets do ot lead to a uque value. Ths s a result of the multtude of errors (maly radom errors) that ca
More informationLower Bounds of the Kirchhoff and Degree Kirchhoff Indices
SCIENTIFIC PUBLICATIONS OF THE STATE UNIVERSITY OF NOVI PAZAR SER. A: APPL. MATH. INFORM. AND MECH. vol. 7, (205), 25-3. Lower Bouds of the Krchhoff ad Degree Krchhoff Idces I. Ž. Mlovaovć, E. I. Mlovaovć,
More informationThe Lie Algebra of Smooth Sections of a T-bundle
IST Iteratoal Joural of Egeerg Scece, Vol 7, No3-4, 6, Page 8-85 The Le Algera of Smooth Sectos of a T-udle Nadafhah ad H R Salm oghaddam Astract: I ths artcle, we geeralze the cocept of the Le algera
More informationExtend the Borel-Cantelli Lemma to Sequences of. Non-Independent Random Variables
ppled Mathematcal Sceces, Vol 4, 00, o 3, 637-64 xted the Borel-Catell Lemma to Sequeces of No-Idepedet Radom Varables olah Der Departmet of Statstc, Scece ad Research Campus zad Uversty of Tehra-Ira der53@gmalcom
More informationMulti Objective Fuzzy Inventory Model with. Demand Dependent Unit Cost and Lead Time. Constraints A Karush Kuhn Tucker Conditions.
It. Joural of Math. Aalyss, Vol. 8, 204, o. 4, 87-93 HIKARI Ltd, www.m-hkar.com http://dx.do.org/0.2988/jma.204.30252 Mult Objectve Fuzzy Ivetory Model wth Demad Depedet Ut Cost ad Lead Tme Costrats A
More informationA New Method for Decision Making Based on Soft Matrix Theory
Joural of Scetfc esearch & eports 3(5): 0-7, 04; rtcle o. JS.04.5.00 SCIENCEDOMIN teratoal www.scecedoma.org New Method for Decso Mag Based o Soft Matrx Theory Zhmg Zhag * College of Mathematcs ad Computer
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 informationLINEAR RECURRENT SEQUENCES AND POWERS OF A SQUARE MATRIX
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 6 2006, #A12 LINEAR RECURRENT SEQUENCES AND POWERS OF A SQUARE MATRIX Hacèe Belbachr 1 USTHB, Departmet of Mathematcs, POBox 32 El Ala, 16111,
More informationIsomorphism on Intuitionistic Fuzzy Directed Hypergraphs
Iteratoal Joral of Scetfc ad Research Pblcatos, Volme, Isse, March 0 ISSN 50-5 Isomorphsm o Ittostc Fzzy Drected Hypergraphs R.Parath*, S.Thlagaath*,K.T.Ataasso** * Departmet of Mathematcs, Vellalar College
More informationEQUIENERGETIC COMPLEMENT GRAPHS
67 Kragujevac J. Sc. 7 005) 67-74. EQUIENERGETIC COMPLEMENT GRAPHS Harshchadra S. Ramae a, Iva Gutma b, Haumappa B. Walkar c ad Sabeea B. Halkar c a Departmet of Mathematcs, Gogte Isttute of Techology,
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 informationMean is only appropriate for interval or ratio scales, not ordinal or nominal.
Mea Same as ordary average Sum all the data values ad dvde by the sample sze. x = ( x + x +... + x Usg summato otato, we wrte ths as x = x = x = = ) x Mea s oly approprate for terval or rato scales, ot
More informationExercises for Square-Congruence Modulo n ver 11
Exercses for Square-Cogruece Modulo ver Let ad ab,.. Mark True or False. a. 3S 30 b. 3S 90 c. 3S 3 d. 3S 4 e. 4S f. 5S g. 0S 55 h. 8S 57. 9S 58 j. S 76 k. 6S 304 l. 47S 5347. Fd the equvalece classes duced
More informationE be a set of parameters. A pair FE, is called a soft. A and GB, over X is the soft set HC,, and GB, over X is the soft set HC,, where.
The Exteso of Sgular Homology o the Category of Soft Topologcal Spaces Sad Bayramov Leoard Mdzarshvl Cgdem Guduz (Aras) Departmet of Mathematcs Kafkas Uversty Kars 3600-Turkey Departmet of Mathematcs Georga
More informationChapter 4 Multiple Random Variables
Revew for the prevous lecture: Theorems ad Examples: How to obta the pmf (pdf) of U = g (, Y) ad V = g (, Y) Chapter 4 Multple Radom Varables Chapter 44 Herarchcal Models ad Mxture Dstrbutos Examples:
More informationA Note on Ratio Estimators in two Stage Sampling
Iteratoal Joural of Scetfc ad Research Publcatos, Volume, Issue, December 0 ISS 0- A ote o Rato Estmators two Stage Samplg Stashu Shekhar Mshra Lecturer Statstcs, Trdet Academy of Creatve Techology (TACT),
More informationA NEW LOG-NORMAL DISTRIBUTION
Joural of Statstcs: Advaces Theory ad Applcatos Volume 6, Number, 06, Pages 93-04 Avalable at http://scetfcadvaces.co. DOI: http://dx.do.org/0.864/jsata_700705 A NEW LOG-NORMAL DISTRIBUTION Departmet of
More informationIntegral Root Labeling of Graphs 1 V.L. Stella Arputha Mary & 2 N. Nanthini
International Journal of Mathematics Trends and Technology (IJMTT) Volume Number - February 08 Integral Root Labeling of Graphs V.L. Stella Arputha Mary & N. Nanthini Department of Mathematics, St. Mary
More informationA Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions
Appled Matheatcs, 1, 4, 8-88 http://d.do.org/1.4/a.1.448 Publshed Ole Aprl 1 (http://www.scrp.org/joural/a) A Covetoal Approach for the Soluto of the Ffth Order Boudary Value Probles Usg Sth Degree Sple
More informationIdeal multigrades with trigonometric coefficients
Ideal multgrades wth trgoometrc coeffcets Zarathustra Brady December 13, 010 1 The problem A (, k) multgrade s defed as a par of dstct sets of tegers such that (a 1,..., a ; b 1,..., b ) a j = =1 for all
More informationSUBCLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH SALAGEAN DERIVATIVE. Sayali S. Joshi
Faculty of Sceces ad Matheatcs, Uversty of Nš, Serba Avalable at: http://wwwpfacyu/float Float 3:3 (009), 303 309 DOI:098/FIL0903303J SUBCLASS OF ARMONIC UNIVALENT FUNCTIONS ASSOCIATED WIT SALAGEAN DERIVATIVE
More informationOn quaternions with generalized Fibonacci and Lucas number components
Polatl Kesm Advaces Dfferece Equatos (205) 205:69 DOI 0.86/s3662-05-05-x R E S E A R C H Ope Access O quateros wth geeralzed Fboacc Lucas umber compoets Emrah Polatl * Seyhu Kesm * Correspodece: emrah.polatl@beu.edu.tr
More informationOdd-even sum labeling of some graphs
International Journal of Mathematics and Soft Computing Vol.7, No.1 (017), 57-63. ISSN Print : 49-338 Odd-even sum labeling of some graphs ISSN Online : 319-515 K. Monika 1, K. Murugan 1 Department of
More informationCHAPTER 4 RADICAL EXPRESSIONS
6 CHAPTER RADICAL EXPRESSIONS. The th Root of a Real Number A real umber a s called the th root of a real umber b f Thus, for example: s a square root of sce. s also a square root of sce ( ). s a cube
More informationFourth Order Four-Stage Diagonally Implicit Runge-Kutta Method for Linear Ordinary Differential Equations ABSTRACT INTRODUCTION
Malasa Joural of Mathematcal Sceces (): 95-05 (00) Fourth Order Four-Stage Dagoall Implct Ruge-Kutta Method for Lear Ordar Dfferetal Equatos Nur Izzat Che Jawas, Fudzah Ismal, Mohamed Sulema, 3 Azm Jaafar
More informationAN UPPER BOUND FOR THE PERMANENT VERSUS DETERMINANT PROBLEM BRUNO GRENET
AN UPPER BOUND FOR THE PERMANENT VERSUS DETERMINANT PROBLEM BRUNO GRENET Abstract. The Permaet versus Determat problem s the followg: Gve a matrx X of determates over a feld of characterstc dfferet from
More informationBeam Warming Second-Order Upwind Method
Beam Warmg Secod-Order Upwd Method Petr Valeta Jauary 6, 015 Ths documet s a part of the assessmet work for the subject 1DRP Dfferetal Equatos o Computer lectured o FNSPE CTU Prague. Abstract Ths documet
More informationResearch Article On the Number of Spanning Trees of Graphs
e Scetfc World Joural, Artcle ID 294038, 5 pages http://dxdoorg/055/204/294038 Research Artcle O the Number of Spag Trees of Graphs F Burcu Bozkurt ad DurmuG Bozkurt Departmet of Mathematcs, Scece Faculty,
More informationStrong Convergence of Weighted Averaged Approximants of Asymptotically Nonexpansive Mappings in Banach Spaces without Uniform Convexity
BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY Bull. Malays. Math. Sc. Soc. () 7 (004), 5 35 Strog Covergece of Weghted Averaged Appromats of Asymptotcally Noepasve Mappgs Baach Spaces wthout
More informationHypersurfaces with Constant Scalar Curvature in a Hyperbolic Space Form
Hypersurfaces wth Costat Scalar Curvature a Hyperbolc Space Form Lu Xm ad Su Wehog Abstract Let M be a complete hypersurface wth costat ormalzed scalar curvature R a hyperbolc space form H +1. We prove
More informationSolution of General Dual Fuzzy Linear Systems. Using ABS Algorithm
Appled Mathematcal Sceces, Vol 6, 0, o 4, 63-7 Soluto of Geeral Dual Fuzzy Lear Systems Usg ABS Algorthm M A Farborz Aragh * ad M M ossezadeh Departmet of Mathematcs, Islamc Azad Uversty Cetral ehra Brach,
More informationComparing Different Estimators of three Parameters for Transmuted Weibull Distribution
Global Joural of Pure ad Appled Mathematcs. ISSN 0973-768 Volume 3, Number 9 (207), pp. 55-528 Research Ida Publcatos http://www.rpublcato.com Comparg Dfferet Estmators of three Parameters for Trasmuted
More informationResearch Article Gauss-Lobatto Formulae and Extremal Problems
Hdaw Publshg Corporato Joural of Iequaltes ad Applcatos Volume 2008 Artcle ID 624989 0 pages do:055/2008/624989 Research Artcle Gauss-Lobatto Formulae ad Extremal Problems wth Polyomals Aa Mara Acu ad
More informationOn the Primitive Classes of K * KHALED S. FELALI Department of Mathematical Sciences, Umm Al-Qura University, Makkah Al-Mukarramah, Saudi Arabia
JKAU: Sc., O vol. the Prmtve, pp. 55-62 Classes (49 of A.H. K (BU) / 999 A.D.) * 55 O the Prmtve Classes of K * (BU) KHALED S. FELALI Departmet of Mathematcal Sceces, Umm Al-Qura Uversty, Makkah Al-Mukarramah,
More informationPTAS for Bin-Packing
CS 663: Patter Matchg Algorthms Scrbe: Che Jag /9/00. Itroducto PTAS for B-Packg The B-Packg problem s NP-hard. If we use approxmato algorthms, the B-Packg problem could be solved polyomal tme. For example,
More informationUnimodality Tests for Global Optimization of Single Variable Functions Using Statistical Methods
Malaysa Umodalty Joural Tests of Mathematcal for Global Optmzato Sceces (): of 05 Sgle - 5 Varable (007) Fuctos Usg Statstcal Methods Umodalty Tests for Global Optmzato of Sgle Varable Fuctos Usg Statstcal
More informationComplete Convergence for Weighted Sums of Arrays of Rowwise Asymptotically Almost Negative Associated Random Variables
A^VÇÚO 1 32 ò 1 5 Ï 2016 c 10 Chese Joural of Appled Probablty ad Statstcs Oct., 2016, Vol. 32, No. 5, pp. 489-498 do: 10.3969/j.ss.1001-4268.2016.05.005 Complete Covergece for Weghted Sums of Arrays of
More informationRADIO NUMBER FOR CROSS PRODUCT P n (P 2 ) Gyeongsang National University Jinju, , KOREA 2,4 Department of Mathematics
Iteratioal Joural of Pure ad Applied Mathematics Volume 97 No. 4 014, 515-55 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://www.ijpam.eu doi: http://dx.doi.org/10.173/ijpam.v97i4.11
More informationarxiv: v4 [math.nt] 14 Aug 2015
arxv:52.799v4 [math.nt] 4 Aug 25 O the propertes of terated bomal trasforms for the Padova ad Perr matrx sequeces Nazmye Ylmaz ad Necat Tasara Departmet of Mathematcs, Faculty of Scece, Selcu Uversty,
More informationNeville Robbins Mathematics Department, San Francisco State University, San Francisco, CA (Submitted August 2002-Final Revision December 2002)
Nevlle Robbs Mathematcs Departmet, Sa Fracsco State Uversty, Sa Fracsco, CA 943 (Submtted August -Fal Revso December ) INTRODUCTION The Lucas tragle s a fte tragular array of atural umbers that s a varat
More informationDifference Cordial Labeling of Graphs Obtained from Double Snakes
International Journal of Mathematics Research. ISSN 0976-5840 Volume 5, Number 3 (013), pp. 317-3 International Research Publication House http://www.irphouse.com Difference Cordial Labeling of Graphs
More informationZ 4p - Magic labeling for some special graphs
Internatonal Journal of Mathematcs and Soft Computng Vol., No. (0, 6-70. ISSN Prnt : 49-8 Z 4p - Magc labelng for some specal graphs ISSN Onlne: 9-55 V.L. Stella Arputha Mary Department of Mathematcs,
More information