The signless Laplacian spread

The signless Laplacian spread of G is defined as SQ(G)=μ1(G)-μn(G), where μ1(G) and μn(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.