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