Harary index and some Hamiltonian properties of graphs
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.
scientific article; zbMATH DE number 6520418