复合图的乘权Harary指数

On the multiplicatively weighted Harary index of composite graphs

分子图的乘权Harary指数H_M(G),被定义为HM(G)=Σ{u,v}⊆V(G)dG(u)dG(v)/dG(u,v),其中d_G(u)表示图G中顶点u的度,d_G(u,v)表示图G中顶点u和v之间的距离.本文主要研究4种图操作下得到的复合图的乘权Harary指数,以及在4种图操作下一些特殊复合图的乘权Harary指数的上下界.

Let H_M(G)be the multiplicatively weighted Harary index of the molecular graph G,which is defined as HM(G)=Σ{u,v}⊆V(G)dG(u)dG(v)/dG(u,v)is the degree of a vertex u∈V(G),and the d_G(u,v)denotes the distance between u and v in G.We introduce four graph operations and obtain explicit formulas for the values of multiplicatively weighted Harary index of composite graphs generated by the four graph operations.Based on this,a lower and an upper bound is determined for the multiplicatively weighted Harary index among graphs in each of the four classes of composite graphs.