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.
Signless Laplacian eigenvalues and circumference of graphs / Wang, Jianfeng; Belardo, Francesco. - In: DISCRETE APPLIED MATHEMATICS. - ISSN 0166-218X. - 161:10-11(2013), pp. 1610-1617. [10.1016/j.dam.2013.01.013]
Signless Laplacian eigenvalues and circumference of graphs
BELARDO, Francesco
2013
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.File | Dimensione | Formato | |
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