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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
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
Electrical & Electronics Engineering

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Harary index of bipartite graphs Hanyuan Deng; Selvaraj Balachandran; Suresh Elumalai; Toufik Mansour
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2019.7.2.12

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.
Co-Authors Hanyuan Deng Suresh Elumalai Toufik Mansour