Harary index and some Hamiltonian properties of graphs (Q896102)
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scientific article; zbMATH DE number 6520418
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Harary index and some Hamiltonian properties of graphs |
scientific article; zbMATH DE number 6520418 |
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Harary index and some Hamiltonian properties of graphs (English)
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11 December 2015
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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.
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Harary index
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Hamiltonian graph
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Hamilton-connected graph
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