Signless Laplacian eigenvalues and circumference of graphs

Authors:
Jianfeng Wang;Francesco Belardo
Affiliations:
Department of Mathematics, QingHai Normal University, XiNing, QingHai 810008, PR China;Department of Mathematics and Computer Science, University of Messina, 98166 Sant'Agata, Messina, Italy
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 7
Cited 0

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Abstract

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 graphs, as induced subgraphs, with respect to the latter property.