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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Suresh Elumalai
Department of Mathematics, University of Haifa, 3498838 Haifa, Israel
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 Selvaraj Balachandran Toufik Mansour