Harary index of bipartite graphs

Hanyuan Deng, Selvaraj Balachandran, Suresh Elumalai, Toufik Mansour

Abstract


Let G be a connected graph with vertex set V(G). The Harary index of a graph is defined as H(G) = ∑u ≠ v 1/d(u, v), where d(u, v) denotes the distance between u and v. In this paper, we determine the extremal graphs with the maximum Harary index among all bipartite graphs of order n with a given matching number, with a given vertex-connectivity and with a given edge-connectivity, respectively.


Keywords


Harary index, bipartite graph, matching number, vertex-connectivity, edge-connectivity

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DOI: http://dx.doi.org/10.5614/ejgta.2019.7.2.12

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