Harary index of bipartite graphs

Hanyuan Deng (College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P.R. China)
Selvaraj Balachandran (Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa, and Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University, Thanjavur, India)
Suresh Elumalai (Department of Mathematics, University of Haifa, 3498838 Haifa, Israel)
Toufik Mansour (Department of Mathematics, University of Haifa, 3498838 Haifa, Israel)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications

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.