Elsevier

Discrete Mathematics

Volume 310, Issues 17–18, 28 September 2010, Pages 2249-2257
Discrete Mathematics

Trees with a given order and matching number that have maximum general Randić index

https://doi.org/10.1016/j.disc.2010.04.028Get rights and content
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Abstract

The general Randić index Rα(G) of a graph G is defined by Rα(G)=uv(d(u)d(v))α, where d(u) is the degree of a vertex u, and the summation extends over all edges uv of G. Some results on trees with a given order and matching number that have minimum general Randić index have been obtained. However, the corresponding maximum problem has not been studied, and usually the maximum problem is much harder than the minimum one. In this paper, we characterize the structure of the trees with a given order and matching number that have maximum general Randić index for α>1 and give a sharp upper bound for 0<α1.

Keywords

General Randić index
Tree
Matching

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Supported by PCSIRT, NSFC and the “973” program.