最大度至少为9的平面图的弱邻点可区别边色数.pdf

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1、第31卷第2期苏州科技学院学报(自然科学版)Vo1．31No．22014年6月JournalofSuzhouUniversityofScienceandT~chnology(NaturalScience)Jun．2014Weakadjacentvertexdistinguishingedge,-coloringsofIplanargraphswithA≥9YANChengchao，HUANGDanjun(CollegeofMathematics，PhysicsandInformationEngineer

2、ing，ZhejiangNormalUniversity，Jinhua321004，China)Abstract：Thispaperintroducesatypeofadjacentvertexdistinguishingedge-coloring，weakadjacentvertexdistinguish-ingedge-oloring．Theweakadjacentvertexdistinguishingedge—coloringofgraphGisaproperedge—coloringofGsu

3、chthatanypairofadjacentA-verticesandseedistinctsetsofcolors．Theminimumnumberofcolorsrequiredforaweakadjacentvertexdistinguishingedge-coloringofGisdenotedbyx(G)．WeprovethatifGisaplanargraphwith△≥9，thenX(G)≤A+2．Keywords：weakadjacentvertexdistinguishingedge

4、-coloring；adjacentvertexdistinguishingedge-coloring；planargraph；m~imumdegreeChineseLibraryClassification：0157．5MR(2000)SubjectClassification：05C15LiteratureLabelCode：APaperNumber：1672—0687(2014)02—0o17—101IntroductionAllgraphsconsideredinthispaperaresimp

5、leandfinite．AplanegraphisaparticulardrawingofaplanargraphontheEuclideanplane．LetV(G)，E(G)，F(G)，A(G)(forshort，A)bevertexset，edgeset，faceset，andmaximumdegreeofagivenplanegraphG，respectively．For∈V(G)，letd(v)denotethedegreeof．Moreover，avertexofdegreekiscalle

6、dak-vertex．Aproperk-edge—coloringisamapping：E(G)_÷{1，2，⋯，kJsuchthat咖(e)≠(e)foranytwoadjacentedgeseande．Thechromaticindex(G)，isthesmallestintegerksuchthatagraphGhasaproperk-edge-coloring．Letv)={(口)Ixv∈E(G)Jdenotethesetofcolorsassignedtoedgesincidenttovert

7、ex，andcallitthecolorsetof．Aproper一edge—co1oring咖ofGisweakadjacentvertexdistinguishing，orak-weak-avd-coloringinshort，ifu)≠()wheneveruv∈(G)andd(u)=()=△．Wecalltwoaajacent△一verticesuandconictunderanedge-coloring4~(orsimplyconict)if()=()．Theweakadjacentvertex

8、distinguish-ingchromaticindex，denotedbyx(G)，isthesmallestintegerksuchthatGhasa一weak—avd—col0ring．Theweak—avd—coloringisarelaxationoftwographparameters：vertexdistin—guishingedgecoloringandadjacentvertexdistinguishingedgecol