Total Prime Graph. Abstract: We introduce a new type of labeling known as Total Prime Labeling. Graphs which admit a Total Prime labeling are
|
|
- Claire Hamilton
- 6 years ago
- Views:
Transcription
1 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 Dpt. of Mathmatcs, Maomaam Sudaraar Uvrsty, Trulvl Abstract: W troduc a w typ of lablg kow as Total Prm Lablg. Graphs whch admt a Total Prm lablg ar P K calld Total Prm Graph. Proprts of ths lablg ar studd ad w hav provd that Paths, Star 1,, Bstar, C Comb, Cycls H K whr s v, Hlm,,, t C ad Fa graph ar Total Prm Graph. W also prov that ay cycl C whr s odd s ot a Total Prm Graph. Kywords: Prm Lablg, Vrtx prm lablg, Total Prm Lablg, Total Prm Graph 1. Itroducto By a graph G = (V,E) w ma a ft, smpl ad udrctd graph. I a Graph G, V(G) dots th vrtx st ad E(G) dots th dg st. Th ordr ad sz of G ar dotd by p ad q rspctvly. Th trmology followd ths papr s accordg to [1]. A lablg of a graph s a map that carrs graph lmts to umbrs. A complt survy of graph lablg s []. Prm lablg ad vrtx prm lablg ar troducd [4] ad [6]. Combg ths two, w df a total prm lablg. Two tgrs a ad b ar sad to b rlatvly prm f thr gratst commo dvsor s 1, (..) ab, 1. Ifa, a 1, for all 1, th th umbrs a1, a, a,, a ar sad to b rlatvly prm pars. Rlatvly prm umbrs play a vtal rol both aalytc ad algbrac umbr thory. Dfto 1.1 [4] Lt G=(V,E) b a graph wth p vrtcs. A bcto f : V( G) 1,,,, p s sad to b as Prm Lablg f for ach dg =xy th labls assgd to x ad y ar rlatvly prm. A graph whch admts prm lablg s calld Prm Graph. Dfto 1. [6] Lt G=(V,E) b a graph wth p vrtcs ad q dgs. A bcto f : E( G) 1,,,, q s sad to b a Vrtx Prm Lablg, f for ach vrtx of dgr at last two, th gratst commo dvsor of th labls o ts cdt dgs s 1.. Total Prm Graph: Dfto.1 Lt G=(V,E) b a graph wth p vrtcs ad q dgs. A bcto f : V E 1,,,, p q sad to b a Total Prm Lablg f () for ach dg =uv, th labls assgd to u ad v ar rlatvly prm. () for ach vrtx of dgr at last, th gratst commo dvsor of th labls o th cdt dgs s 1. A graph whch admts Total Prm Lablg s calld Total Prm Graph. Exampl. (1) C 4 s a Total Prm Graph s 4 7 Iss (ol) Sptmbr 01 Pag 1588
2 Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu. 5 () C (or) K s ot a Total Prm Graph, bcaus w ca assg oly o v labl to a dg ad o mor v labl to a vrtx. But w hav totally thr v labls ad th thrd v labl ca b assgd thr to ay vrtx ot to ay dg. Not that C has Prm Lablg as wll as Vrtx Prm Lablg. Notatos. (1) ad dots th maxmum ad mmum dgr of a vrtx rspctvly. () () dots th gratst tgr lss tha or qual to. dots th last tgr gratr tha or qual to. (4) g.c.d dots gratst commo dvsor. Thorm.4 Th path P v v v v Proof Lt 1 P s a Total Prm Graph. P has vrtcs ad -1 dgs.. W df f : V E 1,,,,( 1) Clarly f s a bcto. f v,1 f,1 Accordg to ths pattr, th vrtcs ar labld such that for ay dg =uvg, gcd [ f u, f v] 1. Also th dgs ar labld such that for ay vrtx v, th g.c.d of all th dgs cdt wth v s 1. Hc P s a Total Prm graph. Dfto.5 K 1 wth pdt dgs cdt wth 1 Thorm.6 1,, 1 Proof Lt V( K ) u K s a Total Prm Graph. 1 ad v,1 b th vrtcs adact to u. Thrfor K 1, has +1 vrtcs ad dgs. Now w df f : V E 1,,,,( 1) f u Clarly f s a bcto. V( K ) s calld a Star Graph ad s dotd by 1, 1 f v,1 f 1,1 Accordg to ths pattr, K1, s a Total Prm Graph. Dfto.7 Th graph obtad from K 1, ad K1,m by og thr ctrs wth a dg s calld a Bstar ad s dotd by B(,m) Thorm.8 Bstar B(,m) s a Total Prm Graph. V( K ) u, v ad u,1 ; v,1 m b th vrtcs adact to u ad v rspctvly. Proof Lt For 1, uu uv ; for ( ) ( m 1), vv ; 1 Thrfor B(,m) has +m+ vrtcs ad +m+1 dgs. Now w df f : V E 1,,,,( m ). K. Iss (ol) Sptmbr 01 Pag 1589
3 Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu ,1 f u f v f u 1,1 f v m f m,1 ( m 1) Clarly f s a bcto. Accordg to ths pattr, clarly B(,m) s a Total Prm Graph. Dfto.9 A graph obtad by attachg a sgl pdt dg to ach vrtx of a path 1 Comb. Thorm.10 Comb s a Total Prm Graph. Proof Lt G b a Comb obtad from th path by og a vrtx u to v, 1. Th dgs ar labld as follows: For1, 1 vu vv 1 Thrfor G has vrtcs ad -1 dgs. Now df f : V E 1,,,,(4 1) f v 1,1 f u,1 f,1 ( 1) Clarly f s a bcto. Accordg to ths pattr, Comb s a Total Prm Graph. Thorm.11 Cycl C, s v, s a Total Prm Graph. Proof Lt C v v v v v Thrfor C has vrtcs ad dgs. Now w df f : V E 1,,,, Clarly f s a bcto. f v,1 f,1 Accordg to ths pattr, clarly Cycl C, s v, s a Total Prm Graph. Thorm.1 Cycl C, s odd, s ot a Total Prm Graph. Proof Lt C v v v v v Thrfor C has vrtcs ad dgs. Df f : V E 1,,,, P v v v v s calld a Now, o. of v labls avalabl s. For ay coscutv vrtcs, w ca assg at most o v labl ad so, umbr of vrtcs wth v labls s at most. Iss (ol) Sptmbr 01 Pag 1590
4 Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu. 5 Also, out of coscutv dgs, w ca assg at most o v labl ad so th umbr of dgs wth v labls s at most. Thrfor th cssary codto for xstc of total Prm Graph s =. Cas 1: 0mod (..) s a multpl of. Thrfor, ths cas (..) (..) Whch s a cotradcto. Cas : 1mod I ths cas (..) 4 (..) 4 But s odd, so t s ot possbl. mod Cas : 1 I ths cas (..) (..) But s odd, so t s ot possbl. Thrfor Cycl C, s odd, s ot a Total Prm Graph. Dfto.1 Hlm H s a graph obtad from whl by attachg a pdt dg at ach vrtx of -cycl. Thorm.14 Hlm H s a Total Prm Graph. u, u,, u Proof Hr ctr vrtx wll b labld as u ad all th vrtcs o th cycl ar labld as 1. Th corrspodg pdt vrtcs ar labld as v 1, v,, v. Th dgs ar labld as 1,,, startg from th pdt dg cdt at vrtx u 1 ad wth lablg th dg o th cycl altratvly clockws drcto 1,,, ad th spoks of th whls ar labld as 1,,, startg from th dg uu1 ad procdg th clockws drcto. Thrfor Hlm H has +1 vrtcs ad dgs. Now w df f : V E 1,,,,(5 1) f u 1 1 f u 1,1 1 f v,1 f 1,1 Iss (ol) Sptmbr 01 Pag 1591
5 Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu. 5 Clarly f s a bcto. Accordg to ths pattr, clarly Hlm H s a Total Prm Graph. Dfto.15 K m, s a complt bpartt graph wth bpartto X ad Y, whch ay two vrtcs X as wll as ay two vrtcs Y ar o-adact. Also vry vrtx of X s adact to vry vrtx of Y. Thorm.16 K,, s a Total Prm Graph. Proof K m, hav m+ vrtcs ad m dgs. Hr m=. Thrfor K, has + vrtcs ad dgs. Lt X u, u ad Y v v v v v u 1 to 1 1 ad th last dg 1 1,,,,. Th dgs ar labld a cotuous mar startg from 1 v 1 u 1 v u. Now w df f : V E 1,,,,( ) as follows: f u 1,1 Th vrtcs Y v v v v 1,,,, ar parttod to sts as follows: for v ad 0 S v 1, v f v Th dgs ar labld as follows:- Cas 1: s odd () for 0 k 1,1, lt f v ad v S +1, s odd +, s v +1, s of th form 10r- ad r=1,,, u v, 4k1 1 4k1 u v 4k 1 k u v 4k 4k () for 0 k, 4k4 uvk u v, u v, u v () Cas : s v () for 0 k 1, 4k 1 u1v 4k1 u v 4k 1 k u v 4k 4k () for 0 k, 4k4 uvk () uv1 Iss (ol) Sptmbr 01 Pag 159
6 Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu. 5 Th uassgd labls gv thr ordr to th dgs th ordr Clarly f s a bcto. 1,,,,. Accordg to ths pattr, clarly K,, s a Total Prm Graph. t t Dfto.17C dots th o-pot uo of t cycls of lgth. C s also calld as Frdshp Graph (or) Dutch t-wdmll. t Thorm.18 s a Total Prm Graph. C t Proof C has t+1 vrtcs ad t dgs. Lt th vrtx st bv v v v wth ctr vrtx v 0. Lt th dg st b,,,, t 0 1 labl th dgs clockws drcto. Now w df f : V E 1,,,,(5t 1) Clarly f s a bcto. Accordg to ths pattr, clarly C as follows: f v 1,0 t 1 f t 1,1 t t s a Total Prm Graph. Dfto.19 Th fa graph F s dfd as K1 P, Thorm.0 Fa graph F,, s a Total Prm Graph. Proof F has 1 vrtcs ad -1 dgs. f : V E 1,,,, W df v v, 1 For 1 For v1v, 1 Clarly f s a bcto. P s a path of vrtcs.,1 f v 1 f f Accordg to ths pattr, Fa Graph F s a Total Prm Graph. 1,,,, t wth 1 v0v1 ad Rfrcs [1]. F.Harary, Graph Thory, Addso Wsly, Radg, Mass., 197. []. J.A.Galla, A dyamc survy of graph lablg, Elctroc J.Combatorcs, (Jauary 010). []. T.M.Apostol, Itroducto to Aalytc Numbr Thory, Narosa Publshg Hous, [4]. A.Tout, A.N. Dabbouy ad K.Howalla, Prm Lablg of graphs, Natoal Acadmy Scc Lttrs, 11(198), [5]. Fu,H.L ad Huag,K.C (1994) o Prm Lablg Dscrt mathmatcs, North Hollad, 17, [6]. T.Drtsky, S.M.L ad J.Mtchm, o Vrtx prm lablg of graphs graph thory, Combatorcs ad Applcatos Vol.1, J.Alav, G.Chartrad ad O.Ollrma ad A.Schwk, ds, Procdgs 6 th tratoal cofrc Thory ad Applcato of Graphs (Wly, Nwyork,1991) Iss (ol) Sptmbr 01 Pag 159
Independent Domination in Line Graphs
Itratoal Joural of Sctfc & Egrg Rsarch Volum 3 Issu 6 Ju-1 1 ISSN 9-5518 Iddt Domato L Grahs M H Muddbhal ad D Basavarajaa Abstract - For ay grah G th l grah L G H s th trscto grah Thus th vrtcs of LG
More informationDifferent types of Domination in Intuitionistic Fuzzy Graph
Aals of Pur ad Appld Mathmatcs Vol, No, 07, 87-0 ISSN: 79-087X P, 79-0888ol Publshd o July 07 wwwrsarchmathscorg DOI: http://dxdoorg/057/apama Aals of Dffrt typs of Domato Itutostc Fuzzy Graph MGaruambga,
More informationAlmost all Cayley Graphs Are Hamiltonian
Acta Mathmatca Sca, Nw Srs 199, Vol1, No, pp 151 155 Almost all Cayly Graphs Ar Hamltoa Mg Jxag & Huag Qogxag Abstract It has b cocturd that thr s a hamltoa cycl vry ft coctd Cayly graph I spt of th dffculty
More informationCOMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES
COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES DEFINITION OF A COMPLEX NUMBER: A umbr of th form, whr = (, ad & ar ral umbrs s calld a compl umbr Th ral umbr, s calld ral part of whl s calld
More informationAotomorphic Functions And Fermat s Last Theorem(4)
otomorphc Fuctos d Frmat s Last Thorm(4) Chu-Xua Jag P. O. Box 94 Bg 00854 P. R. Cha agchuxua@sohu.com bsract 67 Frmat wrot: It s mpossbl to sparat a cub to two cubs or a bquadrat to two bquadrats or gral
More informationFurther Results on Pair Sum Graphs
Applid Mathmatis, 0,, 67-75 http://dx.doi.org/0.46/am.0.04 Publishd Oli Marh 0 (http://www.sirp.org/joural/am) Furthr Rsults o Pair Sum Graphs Raja Poraj, Jyaraj Vijaya Xavir Parthipa, Rukhmoi Kala Dpartmt
More informationDepartment of Mathematics and Statistics Indian Institute of Technology Kanpur MSO202A/MSO202 Assignment 3 Solutions Introduction To Complex Analysis
Dpartmt of Mathmatcs ad Statstcs Ida Isttut of Tchology Kapur MSOA/MSO Assgmt 3 Solutos Itroducto To omplx Aalyss Th problms markd (T) d a xplct dscusso th tutoral class. Othr problms ar for hacd practc..
More informationChiang Mai J. Sci. 2014; 41(2) 457 ( 2) ( ) ( ) forms a simply periodic Proof. Let q be a positive integer. Since
56 Chag Ma J Sc 0; () Chag Ma J Sc 0; () : 56-6 http://pgscccmuacth/joural/ Cotrbutd Papr Th Padova Sucs Ft Groups Sat Taș* ad Erdal Karaduma Dpartmt of Mathmatcs, Faculty of Scc, Atatürk Uvrsty, 50 Erzurum,
More informationIn 1991 Fermat s Last Theorem Has Been Proved
I 99 Frmat s Last Thorm Has B Provd Chu-Xua Jag P.O.Box 94Bg 00854Cha Jcxua00@s.com;cxxxx@6.com bstract I 67 Frmat wrot: It s mpossbl to sparat a cub to two cubs or a bquadrat to two bquadrats or gral
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 informationInternational Journal of Mathematical Archive-6(5), 2015, Available online through ISSN
Itratoal Joural of Mathmatal Arhv-6), 0, 07- Avalabl ol through wwwjmafo ISSN 9 06 ON THE LINE-CUT TRANSFORMATION RAPHS B BASAVANAOUD*, VEENA R DESAI Dartmt of Mathmats, Karatak Uvrsty, Dharwad - 80 003,
More informationNumerical Method: Finite difference scheme
Numrcal Mthod: Ft dffrc schm Taylor s srs f(x 3 f(x f '(x f ''(x f '''(x...(1! 3! f(x 3 f(x f '(x f ''(x f '''(x...(! 3! whr > 0 from (1, f(x f(x f '(x R Droppg R, f(x f(x f '(x Forward dffrcg O ( x from
More informationThe Equitable Dominating Graph
Intrnational Journal of Enginring Rsarch and Tchnology. ISSN 0974-3154 Volum 8, Numbr 1 (015), pp. 35-4 Intrnational Rsarch Publication Hous http://www.irphous.com Th Equitabl Dominating Graph P.N. Vinay
More information3.4 Properties of the Stress Tensor
cto.4.4 Proprts of th trss sor.4. trss rasformato Lt th compots of th Cauchy strss tsor a coordat systm wth bas vctors b. h compots a scod coordat systm wth bas vctors j,, ar gv by th tsor trasformato
More informationReliability of time dependent stress-strength system for various distributions
IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,
More informationSquare Difference Labeling Of Some Path, Fan and Gear Graphs
Iteratoal Joural of Scetfc & Egeerg Research Volume 4, Issue3, March-03 ISSN 9-558 Square Dfferece Labelg Of Some Path, Fa ad Gear Graphs J.Shama Assstat Professor Departmet of Mathematcs CMS College of
More informationERDOS-SMARANDACHE NUMBERS. Sabin Tabirca* Tatiana Tabirca**
ERDO-MARANDACHE NUMBER b Tbrc* Tt Tbrc** *Trslv Uvrsty of Brsov, Computr cc Dprtmt **Uvrsty of Mchstr, Computr cc Dprtmt Th strtg pot of ths rtcl s rprstd by rct work of Fch []. Bsd o two symptotc rsults
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 informationThe probability of Riemann's hypothesis being true is. equal to 1. Yuyang Zhu 1
Th robablty of Ra's hyothss bg tru s ual to Yuyag Zhu Abstract Lt P b th st of all r ubrs P b th -th ( ) lt of P ascdg ordr of sz b ostv tgrs ad s a rutato of wth Th followg rsults ar gv ths ar: () Th
More informationON THE COMPLEXITY OF K-STEP AND K-HOP DOMINATING SETS IN GRAPHS
MATEMATICA MONTISNIRI Vol XL (2017) MATEMATICS ON TE COMPLEXITY OF K-STEP AN K-OP OMINATIN SETS IN RAPS M FARAI JALALVAN AN N JAFARI RA partmnt of Mathmatcs Shahrood Unrsty of Tchnology Shahrood Iran Emals:
More informationIntroduction to logistic regression
Itroducto to logstc rgrsso Gv: datast D { 2 2... } whr s a k-dmsoal vctor of ral-valud faturs or attrbuts ad s a bar class labl or targt. hus w ca sa that R k ad {0 }. For ampl f k 4 a datast of 3 data
More informationBayesian Shrinkage Estimator for the Scale Parameter of Exponential Distribution under Improper Prior Distribution
Itratoal Joural of Statstcs ad Applcatos, (3): 35-3 DOI:.593/j.statstcs.3. Baysa Shrkag Estmator for th Scal Paramtr of Expotal Dstrbuto udr Impropr Pror Dstrbuto Abbas Najm Salma *, Rada Al Sharf Dpartmt
More informationNEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES
Digst Joural of Naomatrials ad Biostructurs Vol 4, No, March 009, p 67-76 NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES A IRANMANESH a*, O KHORMALI b, I NAJAFI KHALILSARAEE c, B SOLEIMANI
More informationSection 6.1. Question: 2. Let H be a subgroup of a group G. Then H operates on G by left multiplication. Describe the orbits for this operation.
MAT 444 H Barclo Spring 004 Homwork 6 Solutions Sction 6 Lt H b a subgroup of a group G Thn H oprats on G by lft multiplication Dscrib th orbits for this opration Th orbits of G ar th right costs of H
More informationSOME PARAMETERS ON EQUITABLE COLORING OF PRISM AND CIRCULANT GRAPH.
SOME PARAMETERS ON EQUITABLE COLORING OF PRISM AND CIRCULANT GRAPH. K VASUDEVAN, K. SWATHY AND K. MANIKANDAN 1 Dpartmnt of Mathmatics, Prsidncy Collg, Chnnai-05, India. E-Mail:vasu k dvan@yahoo.com. 2,
More informationWorksheet: Taylor Series, Lagrange Error Bound ilearnmath.net
Taylor s Thorm & Lagrag Error Bouds Actual Error This is th ral amout o rror, ot th rror boud (worst cas scario). It is th dirc btw th actual () ad th polyomial. Stps:. Plug -valu ito () to gt a valu.
More informationOn Approximation Lower Bounds for TSP with Bounded Metrics
O Approxmato Lowr Bouds for TSP wth Boudd Mtrcs Mark Karpsk Rchard Schmd Abstract W dvlop a w mthod for provg xplct approxmato lowr bouds for TSP problms wth boudd mtrcs mprovg o th bst up to ow kow bouds.
More informationIranian Journal of Mathematical Chemistry, Vol. 2, No. 2, December 2011, pp (Received September 10, 2011) ABSTRACT
Iraa Joral of Mathatcal Chstry Vol No Dcbr 0 09 7 IJMC Two Tys of Gotrc Arthtc dx of V hylc Naotb S MORADI S BABARAHIM AND M GHORBANI Dartt of Mathatcs Faclty of Scc Arak Ursty Arak 856-8-89 I R Ira Dartt
More informationLecture 1: Empirical economic relations
Ecoomcs 53 Lctur : Emprcal coomc rlatos What s coomtrcs? Ecoomtrcs s masurmt of coomc rlatos. W d to kow What s a coomc rlato? How do w masur such a rlato? Dfto: A coomc rlato s a rlato btw coomc varabls.
More informationSome Results on E - Cordial Graphs
Intrnational Journal of Mathmatics Trnds and Tchnology Volum 7 Numbr 2 March 24 Som Rsults on E - Cordial Graphs S.Vnkatsh, Jamal Salah 2, G.Sthuraman 3 Corrsponding author, Dpartmnt of Basic Scincs, Collg
More informationLucas Test is based on Euler s theorem which states that if n is any integer and a is coprime to n, then a φ(n) 1modn.
Modul 10 Addtonal Topcs 10.1 Lctur 1 Prambl: Dtrmnng whthr a gvn ntgr s prm or compost s known as prmalty tstng. Thr ar prmalty tsts whch mrly tll us whthr a gvn ntgr s prm or not, wthout gvng us th factors
More informationLECTURE 6 TRANSFORMATION OF RANDOM VARIABLES
LECTURE 6 TRANSFORMATION OF RANDOM VARIABLES TRANSFORMATION OF FUNCTION OF A RANDOM VARIABLE UNIVARIATE TRANSFORMATIONS TRANSFORMATION OF RANDOM VARIABLES If s a rv wth cdf F th Y=g s also a rv. If w wrt
More informationChapter 5 Special Discrete Distributions. Wen-Guey Tzeng Computer Science Department National Chiao University
Chatr 5 Scal Dscrt Dstrbutos W-Guy Tzg Comutr Scc Dartmt Natoal Chao Uvrsty Why study scal radom varabls Thy aar frqutly thory, alcatos, statstcs, scc, grg, fac, tc. For aml, Th umbr of customrs a rod
More informationOn Estimation of Unknown Parameters of Exponential- Logarithmic Distribution by Censored Data
saqartvlos mcrbata rovul akadms moamb, t 9, #2, 2015 BULLETIN OF THE GEORGIAN NATIONAL ACADEMY OF SCIENCES, vol 9, o 2, 2015 Mathmatcs O Estmato of Ukow Paramtrs of Epotal- Logarthmc Dstrbuto by Csord
More informationChannel Capacity Course - Information Theory - Tetsuo Asano and Tad matsumoto {t-asano,
School of Iformato Scc Chal Capacty 009 - Cours - Iformato Thory - Ttsuo Asao ad Tad matsumoto Emal: {t-asao matumoto}@jast.ac.jp Japa Advacd Isttut of Scc ad Tchology Asahda - Nom Ishkawa 93-9 Japa http://www.jast.ac.jp
More information07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
More informationIntegral points on hyperbolas over Z: A special case
Itgral pots o hprbolas ovr Z: A spcal cas `Pag of 7 Kostat Zlator Dpartmt of Mathmatcs ad Computr Scc Rhod Islad Collg 600 Mout Plasat Avu Provdc, R.I. 0908-99, U.S.A. -mal addrss: ) Kzlator@rc.du ) Kostat_zlator@ahoo.com
More informationMath Tricks. Basic Probability. x k. (Combination - number of ways to group r of n objects, order not important) (a is constant, 0 < r < 1)
Math Trcks r! Combato - umbr o was to group r o objcts, ordr ot mportat r! r! ar 0 a r a s costat, 0 < r < k k! k 0 EX E[XX-] + EX Basc Probablt 0 or d Pr[X > ] - Pr[X ] Pr[ X ] Pr[X ] - Pr[X ] Proprts
More informationCourse 10 Shading. 1. Basic Concepts: Radiance: the light energy. Light Source:
Cour 0 Shadg Cour 0 Shadg. Bac Coct: Lght Sourc: adac: th lght rg radatd from a ut ara of lght ourc or urfac a ut old agl. Sold agl: $ # r f lght ourc a ot ourc th ut ara omttd abov dfto. llumato: lght
More informationAdagba O Henry /International Journal Of Computational Engineering Research / ISSN: OPERATION ON IDEALS
Adagba O Hry /Itratoal Joural Of Computatoal Egrg Rsarh / ISSN 50 3005 OPERATION ON IDEALS Adagba O Hry, Dpt of Idustral Mathmats & Appld Statsts, Eboy Stat Uvrsty, Abakalk Abstrat W provd bas opratos
More informationCorrelation in tree The (ferromagnetic) Ising model
5/3/00 :\ jh\slf\nots.oc\7 Chaptr 7 Blf propagato corrlato tr Corrlato tr Th (frromagtc) Isg mol Th Isg mol s a graphcal mol or par ws raom Markov fl cosstg of a urct graph wth varabls assocat wth th vrtcs.
More informationASYMPTOTIC AND TOLERANCE 2D-MODELLING IN ELASTODYNAMICS OF CERTAIN THIN-WALLED STRUCTURES
AYMPTOTIC AD TOLERACE D-MODELLIG I ELATODYAMIC OF CERTAI THI-WALLED TRUCTURE B. MICHALAK Cz. WOŹIAK Dpartmt of tructural Mchacs Lodz Uvrsty of Tchology Al. Poltrchk 6 90-94 Łódź Polad Th objct of aalyss
More informationA Measure of Inaccuracy between Two Fuzzy Sets
LGRN DEMY OF SENES YERNETS ND NFORMTON TEHNOLOGES Volum No 2 Sofa 20 Masur of accuracy btw Two Fuzzy Sts Rajkumar Vrma hu Dv Sharma Dpartmt of Mathmatcs Jayp sttut of formato Tchoy (Dmd vrsty) Noda (.P.)
More informationGraphs of q-exponentials and q-trigonometric functions
Grahs of -otals ad -trgoomtrc fuctos Amla Carola Saravga To ct ths vrso: Amla Carola Saravga. Grahs of -otals ad -trgoomtrc fuctos. 26. HAL Id: hal-377262 htts://hal.archvs-ouvrts.fr/hal-377262
More informationChapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1
Chatr Fiv Mor Dimsios 51 Th Sac R W ar ow rard to mov o to sacs of dimsio gratr tha thr Ths sacs ar a straightforward gralizatio of our Euclida sac of thr dimsios Lt b a ositiv itgr Th -dimsioal Euclida
More informationSecond Handout: The Measurement of Income Inequality: Basic Concepts
Scod Hadout: Th Masurmt of Icom Iqualty: Basc Cocpts O th ormatv approach to qualty masurmt ad th cocpt of "qually dstrbutd quvalt lvl of com" Suppos that that thr ar oly two dvduals socty, Rachl ad Mart
More informationOn spanning trees and cycles of multicolored point sets with few intersections
On spanning trs and cycls of multicolord point sts with fw intrsctions M. Kano, C. Mrino, and J. Urrutia April, 00 Abstract Lt P 1,..., P k b a collction of disjoint point sts in R in gnral position. W
More informationUnbalanced Panel Data Models
Ubalacd Pal Data odls Chaptr 9 from Baltag: Ecoomtrc Aalyss of Pal Data 5 by Adrás alascs 4448 troducto balacd or complt pals: a pal data st whr data/obsrvatos ar avalabl for all crosssctoal uts th tr
More informationCounting the compositions of a positive integer n using Generating Functions Start with, 1. x = 3 ), the number of compositions of 4.
Coutg th compostos of a postv tgr usg Gratg Fuctos Start wth,... - Whr, for ampl, th co-ff of s, for o summad composto of aml,. To obta umbr of compostos of, w d th co-ff of (...) ( ) ( ) Hr for stac w
More informationH2 Mathematics Arithmetic & Geometric Series ( )
H Mathmatics Arithmtic & Gomtric Sris (08 09) Basic Mastry Qustios Arithmtic Progrssio ad Sris. Th rth trm of a squc is 4r 7. (i) Stat th first four trms ad th 0th trm. (ii) Show that th squc is a arithmtic
More informationGroup Codes Define Over Dihedral Groups of Small Order
Malaysan Journal of Mathmatcal Scncs 7(S): 0- (0) Spcal Issu: Th rd Intrnatonal Confrnc on Cryptology & Computr Scurty 0 (CRYPTOLOGY0) MALAYSIA JOURAL OF MATHEMATICAL SCIECES Journal hompag: http://nspm.upm.du.my/ournal
More informationOn the Possible Coding Principles of DNA & I Ching
Sctfc GOD Joural May 015 Volum 6 Issu 4 pp. 161-166 Hu, H. & Wu, M., O th Possbl Codg Prcpls of DNA & I Chg 161 O th Possbl Codg Prcpls of DNA & I Chg Hupg Hu * & Maox Wu Rvw Artcl ABSTRACT I ths rvw artcl,
More informationAdvances of Clar's Aromatic Sextet Theory and Randic 's Conjugated Circuit Model
Th Op Orgac hmstry Joural 0 5 (Suppl -M6) 87-87 Op Accss Advacs of lar's Aromatc Sxtt Thory ad Radc 's ougatd rcut Modl Fu Zhag a Xaofg Guo a ad Hpg Zhag b a School of Mathmatcal Sccs Xam Uvrsty Xam Fua
More informationOn the approximation of the constant of Napier
Stud. Uiv. Babş-Bolyai Math. 560, No., 609 64 O th approximatio of th costat of Napir Adri Vrscu Abstract. Startig from som oldr idas of [] ad [6], w show w facts cocrig th approximatio of th costat of
More informationIntroduction to logistic regression
Itroducto to logstc rgrsso Gv: datast D {... } whr s a k-dmsoal vctor of ral-valud faturs or attrbuts ad s a bar class labl or targt. hus w ca sa that R k ad {0 }. For ampl f k 4 a datast of 3 data pots
More informationGroup Consensus of Second-Order Multi-agent Networks with Multiple Time Delays
Itratoal Cofrc o Appld Mathmatcs, Smulato ad Modllg (AMSM 6) Group Cossus of Scod-Ordr Mult-agt Ntworks wth Multpl Tm Dlays Laghao J* ad Xyu Zhao Chogqg Ky Laboratory of Computatoal Itllgc, Chogqg Uvrsty
More informationWeek 3: Connected Subgraphs
Wk 3: Connctd Subgraphs Sptmbr 19, 2016 1 Connctd Graphs Path, Distanc: A path from a vrtx x to a vrtx y in a graph G is rfrrd to an xy-path. Lt X, Y V (G). An (X, Y )-path is an xy-path with x X and y
More informationcycle that does not cross any edges (including its own), then it has at least
W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th
More informationComplex Numbers. Prepared by: Prof. Sunil Department of Mathematics NIT Hamirpur (HP)
th Topc Compl Nmbrs Hyprbolc fctos ad Ivrs hyprbolc fctos, Rlato btw hyprbolc ad crclar fctos, Formla of hyprbolc fctos, Ivrs hyprbolc fctos Prpard by: Prof Sl Dpartmt of Mathmatcs NIT Hamrpr (HP) Hyprbolc
More informationHadamard Exponential Hankel Matrix, Its Eigenvalues and Some Norms
Math Sci Ltt Vol No 8-87 (0) adamard Exotial al Matrix, Its Eigvalus ad Som Norms İ ad M bula Mathmatical Scics Lttrs Itratioal Joural @ 0 NSP Natural Scics Publishig Cor Dartmt of Mathmatics, aculty of
More informationSuzan Mahmoud Mohammed Faculty of science, Helwan University
Europa Joural of Statstcs ad Probablty Vol.3, No., pp.4-37, Ju 015 Publshd by Europa Ctr for Rsarch Trag ad Dvlopmt UK (www.ajourals.org ESTIMATION OF PARAMETERS OF THE MARSHALL-OLKIN WEIBULL DISTRIBUTION
More informationDerangements and Applications
2 3 47 6 23 Journal of Intgr Squncs, Vol. 6 (2003), Articl 03..2 Drangmnts and Applications Mhdi Hassani Dpartmnt of Mathmatics Institut for Advancd Studis in Basic Scincs Zanjan, Iran mhassani@iasbs.ac.ir
More informationCombinatorial Networks Week 1, March 11-12
1 Nots on March 11 Combinatorial Ntwors W 1, March 11-1 11 Th Pigonhol Principl Th Pigonhol Principl If n objcts ar placd in hols, whr n >, thr xists a box with mor than on objcts 11 Thorm Givn a simpl
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 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 informationRepeated Trials: We perform both experiments. Our space now is: Hence: We now can define a Cartesian Product Space.
Rpatd Trals: As w hav lood at t, th thory of probablty dals wth outcoms of sgl xprmts. I th applcatos o s usually trstd two or mor xprmts or rpatd prformac or th sam xprmt. I ordr to aalyz such problms
More informationSection 5.1/5.2: Areas and Distances the Definite Integral
Scto./.: Ars d Dstcs th Dt Itgrl Sgm Notto Prctc HW rom Stwrt Ttook ot to hd p. #,, 9 p. 6 #,, 9- odd, - odd Th sum o trms,,, s wrtt s, whr th d o summto Empl : Fd th sum. Soluto: Th Dt Itgrl Suppos w
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 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 informationV. 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 informationSearching Linked Lists. Perfect Skip List. Building a Skip List. Skip List Analysis (1) Assume the list is sorted, but is stored in a linked list.
3 3 4 8 6 3 3 4 8 6 3 3 4 8 6 () (d) 3 Sarching Linkd Lists Sarching Linkd Lists Sarching Linkd Lists ssum th list is sortd, but is stord in a linkd list. an w us binary sarch? omparisons? Work? What if
More informationMODEL QUESTION. Statistics (Theory) (New Syllabus) dx OR, If M is the mode of a discrete probability distribution with mass function f
MODEL QUESTION Statstcs (Thory) (Nw Syllabus) GROUP A d θ. ) Wrt dow th rsult of ( ) ) d OR, If M s th mod of a dscrt robablty dstrbuto wth mass fucto f th f().. at M. d d ( θ ) θ θ OR, f() mamum valu
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 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 informationShortest Paths in Graphs. Paths in graphs. Shortest paths CS 445. Alon Efrat Slides courtesy of Erik Demaine and Carola Wenk
S 445 Shortst Paths n Graphs lon frat Sls courtsy of rk man an arola Wnk Paths n raphs onsr a raph G = (V, ) wth -wht functon w : R. Th wht of path p = v v v k s fn to xampl: k = w ( p) = w( v, v + ).
More informationHardy-Littlewood Conjecture and Exceptional real Zero. JinHua Fei. ChangLing Company of Electronic Technology Baoji Shannxi P.R.
Hardy-Littlwood Conjctur and Excptional ral Zro JinHua Fi ChangLing Company of Elctronic Tchnology Baoji Shannxi P.R.China E-mail: fijinhuayoujian@msn.com Abstract. In this papr, w assum that Hardy-Littlwood
More informationChapter 6. pn-junction diode: I-V characteristics
Chatr 6. -jucto dod: -V charactrstcs Tocs: stady stat rsos of th jucto dod udr ald d.c. voltag. ucto udr bas qualtatv dscusso dal dod quato Dvatos from th dal dod Charg-cotrol aroach Prof. Yo-S M Elctroc
More informationBasic Polyhedral theory
Basic Polyhdral thory Th st P = { A b} is calld a polyhdron. Lmma 1. Eithr th systm A = b, b 0, 0 has a solution or thr is a vctorπ such that π A 0, πb < 0 Thr cass, if solution in top row dos not ist
More informationExtension of Two-Dimensional Discrete Random Variables Conditional Distribution
Itratoal Busss Rsarch wwwccstorg/br Extso of Two-Dsoal Dscrt Rado Varabls Codtoal Dstrbuto Fxu Huag Dpartt of Ecoocs, Dala Uvrsty of Tchology Dala 604, Cha E-al: softwar666@63co Chg L Dpartt of Ecoocs,
More informationAn Application of Hardy-Littlewood Conjecture. JinHua Fei. ChangLing Company of Electronic Technology Baoji Shannxi P.R.China
An Application of Hardy-Littlwood Conjctur JinHua Fi ChangLing Company of Elctronic Tchnology Baoji Shannxi P.R.China E-mail: fijinhuayoujian@msn.com Abstract. In this papr, w assum that wakr Hardy-Littlwood
More informationStrongly Connected Components
Strongly Connctd Componnts Lt G = (V, E) b a dirctd graph Writ if thr is a path from to in G Writ if and is an quivalnc rlation: implis and implis s quivalnc classs ar calld th strongly connctd componnts
More informationsignal amplification; design of digital logic; memory circuits
hatr Th lctroc dvc that s caabl of currt ad voltag amlfcato, or ga, cojucto wth othr crcut lmts, s th trasstor, whch s a thr-trmal dvc. Th dvlomt of th slco trasstor by Bard, Bratta, ad chockly at Bll
More informationFrequency hopping sequences with optimal partial Hamming correlation
1 Frqucy hoppg squcs wth optmal partal Hammg corrlato Jgju Bao ad ju J arxv:1511.02924v2 [cs.it] 11 Nov 2015 Abstract Frqucy hoppg squcs (FHSs) wth favorabl partal Hammg corrlato proprts hav mportat applcatos
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 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 informationIntroduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013
18.782 Introduction to Arithmtic Gomtry Fall 2013 Lctur #20 11/14/2013 20.1 Dgr thorm for morphisms of curvs Lt us rstat th thorm givn at th nd of th last lctur, which w will now prov. Thorm 20.1. Lt φ:
More informationTolerance Interval for Exponentiated Exponential Distribution Based on Grouped Data
Itratoal Rfrd Joural of Egrg ad Scc (IRJES) ISSN (Ol) 319-183X, (Prt) 319-181 Volum, Issu 10 (Octobr 013), PP. 6-30 Tolrac Itrval for Expotatd Expotal Dstrbuto Basd o Groupd Data C. S. Kaad 1, D. T. Shr
More informationChapter Discrete Fourier Transform
haptr.4 Dscrt Fourr Trasform Itroducto Rcad th xpota form of Fourr srs s Equatos 8 ad from haptr., wt f t 8, h.. T w t f t dt T Wh th abov tgra ca b usd to comput, h.., t s mor prfrab to hav a dscrtzd
More informationNew families of p-ary sequences with low correlation and large linear span
THE JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOMMUNICATIONS Volu 4 Issu 4 Dcbr 7 TONG X WEN Qao-ya Nw fals of -ary sucs wth low corrlato ad larg lar sa CLC ubr TN98 Docut A Artcl ID 5-8885 (7 4-53-4
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 informationChapter 10. The singular integral Introducing S(n) and J(n)
Chaptr Th singular intgral Our aim in this chaptr is to rplac th functions S (n) and J (n) by mor convnint xprssions; ths will b calld th singular sris S(n) and th singular intgral J(n). This will b don
More informationAPPENDIX: STATISTICAL TOOLS
I. Nots o radom samplig Why do you d to sampl radomly? APPENDI: STATISTICAL TOOLS I ordr to masur som valu o a populatio of orgaisms, you usually caot masur all orgaisms, so you sampl a subst of th populatio.
More informationFolding of Regular CW-Complexes
Ald Mathmatcal Scncs, Vol. 6,, no. 83, 437-446 Foldng of Rgular CW-Comlxs E. M. El-Kholy and S N. Daoud,3. Dartmnt of Mathmatcs, Faculty of Scnc Tanta Unvrsty,Tanta,Egyt. Dartmnt of Mathmatcs, Faculty
More informationSTIRLING'S 1 FORMULA AND ITS APPLICATION
MAT-KOL (Baja Luka) XXIV ()(08) 57-64 http://wwwimviblorg/dmbl/dmblhtm DOI: 075/МК80057A ISSN 0354-6969 (o) ISSN 986-588 (o) STIRLING'S FORMULA AND ITS APPLICATION Šfkt Arslaagić Sarajvo B&H Abstract:
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More informationJOURNAL OF COLLEGE OF EDUCATION NO
NO.3...... 07 Ivrt S-bst Copproxmto -ormd Spcs Slw Slm bd Dprtmt of Mthmtcs Collg of ducto For Pur scc, Ib l-hthm, Uvrsty of Bghdd slwlbud@yhoo.com l Musddk Dlph Dprtmt of Mthmtcs,Collg of Bsc ducto, Uvrsty
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 information8. Queueing systems. Contents. Simple teletraffic model. Pure queueing system
8. Quug sysms Cos 8. Quug sysms Rfrshr: Sml lraffc modl Quug dscl M/M/ srvr wag lacs Alcao o ack lvl modllg of daa raffc M/M/ srvrs wag lacs lc8. S-38.45 Iroduco o Tlraffc Thory Srg 5 8. Quug sysms 8.
More informationBinary Choice. Multiple Choice. LPM logit logistic regresion probit. Multinomial Logit
(c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 3 Bary Choc LPM logt logstc rgrso probt Multpl Choc Multomal Logt (c Pogsa Porchawssul,
More informationEstimation of Population Variance Using a Generalized Double Sampling Estimator
r Laka Joural o Appl tatstcs Vol 5-3 stmato o Populato Varac Us a Gralz Doubl ampl stmator Push Msra * a R. Kara h Dpartmt o tatstcs D.A.V.P.G. Coll Dhrau- 8 Uttarakha Ia. Dpartmt o tatstcs Luckow Uvrst
More information