单圈图(外围)Wiener指标的计算公式  

The(Peripheral)Wiener index of unicyclic graphs

作　　者：李建喜 雷思宇 LI Jian-xi;LEI Si-yu(School of Mathematics and Statistics,Minnan normal University,Zhangzhou,363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《高校应用数学学报（A辑）》2020年第4期495-500,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：福建省自然科学基金(2018J01423)。

摘　　要：设G=(V,E)为简单连通图,图G的Wiener指标和外围Wiener指标分别指图G中所有不同顶点对间的距离之和与所有不同外围顶点对间的距离之和,其中外围顶点指的是到其它顶点的最大距离为图G的直径的点.顶点数目和边数目相同的简单连通图称为单圈图,文中分别给出了单圈图的Wiener指标和外围Wiener指标的计算公式,其形式类似于树图上的(外围)Wiener指标的计算公式.Let G=(V,E)be a simple connected graph.The wiener and the peripheral wiener indies of G respectively are the sum of distances between all pairs of vertices and the sum of distances between all pairs of peripheral vertices of G,where the peripheral vertex refers to the vertex whose maximum distance to other vertices is the diameter of G.A simple connected graph with the same number of vertices and edges is called an unicyclic graph.In this paper,the formulae for computing the wiener index and the peripheral wiener index of unicyclic graphs are deduced,respectively,their forms are similar to the formulae for computing the(peripheral)wiener index of trees.

关 键 词：单圈图 WIENER指标 外围Wiener指标 

分 类 号：O157[理学—数学]