Wiener index versus maximum degree in trees

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Abstract

The Wiener index of a graph is the sum of all pairwise distances of vertices of the graph. In this paper, we characterize the trees which minimize the Wiener index among all trees of given order and maximum degree and the trees which maximize the Wiener index among all trees of given order that have only vertices of two different degrees.

Keywords

Tree
Wiener index
Average distance
Degree
Valency

Cited by (0)

1

Supported by a post-doctoral DONET grant.

2

This research was supported in part by the NSF grant DMS 0072187.