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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 305164, 6 pages
http://dx.doi.org/10.1155/2014/305164
Research Article

Energy Conditions for Hamiltonicity of Graphs

1School of Mathematics & Computation Sciences, Anqing Normal College, Anqing 246011, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 25 December 2013; Accepted 22 January 2014; Published 6 March 2014

Academic Editor: Wenwu Yu

Copyright © 2014 Guidong Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be an undirected simple graph of order . Let be the adjacency matrix of , and let be its eigenvalues. The energy of is defined as . Denote by a bipartite graph. In this paper, we establish the sufficient conditions for having a Hamiltonian path or cycle or to be Hamilton-connected in terms of the energy of the complement of , and give the sufficient condition for having a Hamiltonian cycle in terms of the energy of the quasi-complement of .