Li, Rao Harary index and some Hamiltonian properties of graphs. (English) Zbl 1332.05084 AKCE Int. J. Graphs Comb. 12, No. 1, 64-69 (2015). Let \(G\) be a connected graph. Then the Harary index of \(G\) is defined as \(H(G)=\sum_{u,v\in V(G)}\frac{1}{d_{G}(u,v)},\) where \(d_{v}(u,v)\) is the distance of \(u\), \(v\) in \(G\). In the paper, a sufficient condition for a connected graph to be Hamiltonian (Hamiltonian-connected) is given in terms of the Harary index. Reviewer: Peter Horák (Tacoma) Cited in 8 Documents MSC: 05C45 Eulerian and Hamiltonian graphs 05C40 Connectivity Keywords:Harary index; Hamiltonian graph; Hamilton-connected graph PDFBibTeX XMLCite \textit{R. Li}, AKCE Int. J. Graphs Comb. 12, No. 1, 64--69 (2015; Zbl 1332.05084) Full Text: DOI References: [1] Bondy, J. A.; Murty, U. S.R., Graph Theory with Applications (1976), Macmillan, London and Elsevier: Macmillan, London and Elsevier New York · Zbl 1134.05001 [2] Ivanciuc, O.; Balaban, T. S.; Balaban, A. T., Reciprocal distance matrix, related local vertex invariants and topological indices, J. Math. Chem., 12, 309-318 (1993) [3] Plavšić, D.; Nikolić, S.; Trinajstić, N.; Mihalić, Z., On the Harary index for the characterization of chemical graphs, J. Math. Chem., 12, 235-250 (1993) [4] Hua, H.; Wang, M., On Harary index and traceable graphs, MATCH Commun. Math. Comput. Chem., 70, 297-300 (2013) · Zbl 1299.05091 [5] Byer, W.; Smeltzer, D., Edge bounds in nonhamiltonian \(k\)-connected graphs, Discrete Math., 307, 1572-1579 (2007) · Zbl 1123.05051 [6] Berge, C., Graphs and Hypergraphs (1976), American Elsevier Publishing Company · Zbl 0483.05029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.