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On Harary index
Authors:Bo Zhou  Xiaochun Cai  Nenad Trinajstić
Institution:(1) Department of Mathematics, South China Normal University, Guangzhou, 510631, People’s Republic of China;(2) The Rugjer Bošković Institute, P. O. Box 180, Zagreb, 10002, Croatia
Abstract:We report lower and upper bounds for the Harary index of a connected (molecular) graph, and, in particular, upper bounds of triangle- and quadrangle-free graphs. We also give the Nordhaus–Gaddum-type result for the Harary index. Dedicated to the memory of Professor Frank Harary (1921–2005), the late grandmaster of both graph theory and chemical graph theory.
Keywords:Harary index  Harary matrix  Wiener index  Triangle-free graphs  Quandrangle-free graphs
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