一类单圈图的最大Hosoya指标

摘要

一个图的Hosoya指标Z(G)定义为图G的所有的边独立集数目之和。让Mn 标记圈上所有点的度数不小于3的满载单圈图。本文将分别描述出满载单圈图的第一大和第二大Hosoya指标及其极图特征。%The Hosoya index Z(G) of a graph is defined as the total number of edge independent sets of G. Let Mn be the set of fully loaded unicyclic graphs with the property that there is no vertex with degree less than 3 in its cycle. In this paper, we consider the maximal and second-maximal Hosoya indices of fully loaded unicyclic graphs, and characterize the extremal graphs.