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Harary index and some Hamiltonian properties of graphs. (English) Zbl 1332.05084

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.

MSC:

05C45 Eulerian and Hamiltonian graphs
05C40 Connectivity
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References:

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