满载双圈图的Kirchhoff指标的极值(英文)

The Extremal Kirchhoff Index of Fully Loaded Bicyclic Graph

电阻距离这一概念是由Klein和Randic引入的,一个图的Kirchhoff指标定义为G中所有点对的电阻距离和.满载双圈图是指圈上的所有点的度数不小于3的双圈图.该文给出了满载双圈图的最大,最小Kirchhoff指标并刻画出了与之相对应的极图.

The concept of resistance distance was introduced by Klein and Randic.The Kirchhoff index Kf （G）of a graph G is the sum of resistance distances between all pairs of vertices.A fully loaded bicyclic graph is a bicyclic graph with the property that there is no vertex with degree less than 3 in its two cycles.In this paper,the Kirchhoff index of loaded bicyclic graph is calculated,and the extremal graphs with minimal and maximal Kirchhoff index among all fully loaded bicyclic graph are characterized.