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The signless Laplacian spread. (English) Zbl 1206.05064

The signless Laplacian spread of \(G\) is defined as \(SQ(G) = \mu_1 (G) - \mu_n (G)\), where \(\mu_1 (G)\) and \(\mu_n (G)\) are the maximum and minimum eigenvalues of the signless Laplacian matrix of \(G\), respectively. This paper presents some upper and lower bounds for \(SQ(G)\). Moreover, the unique unicyclic graph with maximum signless Laplacian spread among the class of connected unicyclic graphs of order \(n\) is determined.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A42 Inequalities involving eigenvalues and eigenvectors
15B36 Matrices of integers
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