Received by the editors on July 22, 2010. Accepted for publication on February 17, 2011. Handling Editor: Bryan Shader. School of Mathematical Science, South China Normal University, Guangzhou, 510631, P.R. China ([email protected], Zhifu You; [email protected], Bolian Liu). This work was supported by the NNSF of China (No. 11071088). Electronic Journal of Linear Algebra ISSN 1081-3810 A publi...

In this paper, we investigate the relation between the Q -spectrum and the structure of G in terms of the circumference of G. Exploiting this relation, we give a novel necessary condition for a graph to be Hamiltonian by means of its Q -spectrum. We also determine the graphs with exactly one or two Q -eigenvalues greater than or equal to 2 and obtain all minimal forbidden subgraphs and maximal ...

AMS Mathematics Subject Classification (2000): 05C50

In this paper, we establish a tight sufficient condition for the Hamiltonicity of graphs with large minimum degree in terms of the signless Laplacian spectral radius and characterize all extremal graphs. Moreover, we prove a similar result for balanced bipartite graphs. Additionally, we construct infinitely many graphs to show that results proved in this paper give new strength for one to deter...