Wiener指数,Hyper-Wiener指数,Harary指数与图的β-亏损性

Wiener Index, Hyper-Wiener Index, Harary Index and β-deficient of Graphs

图G的亏损数def(G)是指G中所有顶点个数与它的最大匹配中顶点个数之差,如果def(G)≤β,则称图G是β-亏损的。本文主要利用图的Wiener指数、hyper-Wiener指数、Harary指数,给出了具有最小度条件的连通图是β-亏损的充分条件。

The deficiency of a graph G, denoted by def(G), is the number of vertices unmatched under a maximum matching in G. We call G β- deficient if def(G)≤β. In this paper, In terms of Wiener index, Hyper-Wiener index, Harary index of graph, it is given that the connected graph with the minimum condition is a sufficient condition for β-deficient.