关于树的离心距离和的极值.pdf

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7、''………ccc:l%ålÚ;ä;››ê;Õáê;š;{šIAbstractTheeccentricdistancesumofgraphisanactiveandimportantfieldingraphtheo-ry,theresearchontheeccentricdistancesumoftreehasbecomeahottopicinspectraltheeccentricdistancesumofgraph.In1957,H.Wienerposedtheproblemofatopo-logicalindex

8、.Thisproblemhasreceivedmuchattentioninmathematics.ThewienerindexisdefinedasthesumofalldistancesbetweenunorderedpairsofPverticesW(G)=d(u;v).Theeccentricity"G(v)ofavertexvisthemaximumu;v2VGdistancefromvtoanyothervertex.DG(v)isthesumofalldistancesfromthevertexPv.Thee

9、ccentricdistancesumofGisdefinedasd(G)="(v)D(v),where"(v)GGPv2VGistheeccentricityofthevertexvandDG(v)=vG(u;v)isthemaximumdistanceu2Vfromvtoanyothervertex.Thespe