Elsevier

Discrete Applied Mathematics

Volume 251, 31 December 2018, Pages 160-170
Discrete Applied Mathematics

Maximum Resistance-Harary index of cacti

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Abstract

The Resistance-Harary index of a connected graph G is defined as RH(G)={u,v}V(G)1rG(u,v), where rG(u,v) is the resistance distance between vertices u andv in G. A connected graph G is said to be a cactus if each of its blocks is either an edge or a cycle. Let Cnk be the set of all cacti of order n containing exactly k cycles. In this paper, we characterize the graphs with maximum Resistance-Harary index among all graphs in Cnk.

Keywords

Cactus
Resistance distance
Resistance-Harary index

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Supported by National Natural Science Foundation of China (11771016, 11601006, 11571315), Project of Educational Department of Anhui Province (KJ2016A044).