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
BELARDO, FRANCESCO
2013-01-01
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 in questo prodotto:
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