【摘 要】
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In this report, we introduce a relation between the Q-spectrum and the structure of G by the circumference of G.Exploiting this relation, we give a new nece
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In this report, we introduce a relation between the Q-spectrum and the structure of G by the circumference of G.Exploiting this relation, we give a new necessary condition for a graph not to be Hamiltonian by its Q-spectrum, determine all connected graphs with exactly one or two Q-eigenvalues greater than 2 and obtain all maximal forbidden subgraphs with respect to the latter property, and characterize all connected graphs with exactly three Q-eigenvalues at least 2 and obtain all minimal forbidden subgraphs with respect to this property.In addition, we characterize all connected graphs with the first three largest Q-eigenvalues respectively equal to 2.
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