For a simple graph G, let NCD(G)=min{|N(u)@?N(v)|+d(w):u,v,w@?V(G),uv@?@?E(G),wvorwu@?@?E(G)}. In this paper, we prove that if NCD(G)>=|V(G)|, then either G is Hamiltonian-connected, or G belongs to a well-characterized class of graphs. The former results by Dirac, Ore and Faudree et al. are extended.
['Zhao Ke-wen', 'Hong-Jian Lai', 'Ju Zhou']
Hamiltonian-connected graphs