Original scientific paper

The Hosoya-Wiener Polynomial of Weighted Trees

Blaž Zmazek
Janez Žerovnik

Abstract

Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex
weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-
Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula
for computing the Hosoya-Wiener polynomial of a weighted tree is given.

Keywords

Hosoya-Wiener polynomial; vertex weighted graphs; weighted tree

Hrčak ID:

12827

URI

https://hrcak.srce.hr/12827

Publication date:

11.3.2007.

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