树按Wiener指标的排序

Ordering Trees by Their Wiener Indices

n个顶点的树的集合记为Tn.连通图G的Wiener指标等于图G中任意两点的距离和.本文考虑Tn中树的按Wie ner指标排序的问题.先对Tn中树按非悬挂边的数目分类,确定出具有1条非悬挂边,2条非悬挂边,和3条非悬挂边的树包括的图类.根据Wiener指标的计算公式及文中提到的变换方式,得到这些图类的序关系.基于这些序关系,确定了Tn中具有最小Wiener指标的前15个树.

The set of trees with n vertices is denoted byT_n .In this paper,the problem of ordering trees inT_n by their Wiener indices is considered.At first,a partition for trees inT_n is given by the number of nonpendent edges.And the trees with one nonpendent edge,two nonpendent edges,and three nonpendent edges,respectively,contain four kinds of trees.According to the calculation formular and transformation,some order relations of these four kinds of trees inT_n are obtained. Base on the order relations,the trees inT_n with the first up to fifteenth smallest Wiener indices are determined.