Harary index of bipartite graphs - Hanyuan Deng; Selvaraj Balachandran; Suresh Elumalai; Toufik Mansour (Electronic Journal of Graph Theory and Applications (EJGTA), 2019)
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.