, Volume 91, Issue 2, pp 119-132
Date: 08 Apr 2006

A Class of Trees and its Wiener Index

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Abstract

In this paper, we will consider the Wiener index for a class of trees that is connected to partitions of integers. Our main theorem is the fact that every integer \(\geq 470\) is the Wiener index of a member of this class. As a consequence, this proves a conjecture of Lepović and Gutman. The paper also contains extremal and average results on the Wiener index of the studied class.

This work was supported by Austrian Science Fund project no. S-8307-MAT.