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

Published online by Cambridge University Press:  19 September 2013

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
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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 $6$.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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