给定悬挂点的三圈图的零阶广义Randic指数

Zeroth-order General Randic Index of Tricyclic Graphs with Given Pendent Vertices

对于简单的连通图G,它的零阶广义Randic指数0Rα(G)定义为Σv∈V(G)[dG(v)]α,其中α是一个给定的实数,dG(v)是G中顶点v的度.简单连通图G的零阶广义Randic指数是化学图论中一个重要的拓扑指数,其在化学领域中有着广泛的研究及应用.基于此对于任意的α(≠0,1),它给出了顶点个数为n,悬挂点为k的所有三圈图的零阶广义Randic指数0Rα的一些紧的界.

Let G be a simply connected graph and a be a given real number,the zeroth-order general Randic index o of Re（G） is defined as （c）[dc（v） ] , where a is a given real number and dc（v） denotes the degreeof the vertex v of G. The zeroth-order general Randic index of the simply connected graph G is one of the most important topological indices in chemical graph theory, it has been extensively studied and applied in the field ofchemistry. Based on such situation,it gives sharp bounds of the zeroth-order general Randic index 0Ra （G） of all tricyclic graphs with n vertices and k pendent vertices,where a≠0, 1.