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WIENER INDEX OF TREES OF GIVEN ORDER AND DIAMETER AT MOST $6$

Part of: Graph theory

Published online by Cambridge University Press:  19 September 2013

SIMON MUKWEMBI  and
TOMÁŠ VETRÍK
SIMON MUKWEMBI
Affiliation:
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa email [email protected]
TOMÁŠ VETRÍK*
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa
*
✉[email protected]
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Abstract

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The long-standing open problem of finding an upper bound for the Wiener index of a graph in terms of its order and diameter is addressed. Sharp upper bounds are presented for the Wiener index, and the related degree distance and Gutman index, for trees of order $n$ and diameter at most $6$.

Keywords

Wiener indexdegree distanceGutman indextreediameter

MSC classification

Secondary: 05C12: Distance in graphs 05C05: Trees 05C07: Vertex degrees
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 3 , June 2014 , pp. 379 - 396
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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