Hamiltonian-connected graphs

Authors:
Zhao Kewen;Hong-Jian Lai;Ju Zhou
Affiliations:
Department of Mathematics, Qiongzhou University, Wuzhishan, Hainan, 572200, China and Department of Mathematics, Hainan Normal University, Haikou, Hainan, 571100, China;Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA;Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

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.