Harary index and some Hamiltonian properties of graphs

For a nontrivial connected graph GG, its Harary index H(G)H(G) is defined as ∑{u,v}⊆V(G)1dG(u,v), where dG(u,v)dG(u,v) is the distance between vertices uu and vv. Hua and Wang (2013), using Harary index, obtained a sufficient condition for the traceable graphs. In this note, we use Harary index to present sufficient conditions for Hamiltonian and Hamilton-connected graphs.