Maximum Resistance-Harary index of cacti

Abstract The Resistance-Harary index of a connected graph G is defined as R H ( G ) = ∑ { u , v } ⊆ V ( G ) 1 r G ( u , v ) , where r G ( u , v ) is the resistance distance between vertices u and v 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 C n k 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 C n k .

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