The maximum signless Laplacian separator of tricyclic and quadricyclic graphs

Let G be a graphs of order n and q1(G)≥q2(G)≥…≥qn(G) be its Q-eigenvalues. The signless Laplacian separator SQ(G) of G is defined as SQ(G)=q1(G)-q2(G). The maximum signless Laplacian separator of tricyclic and quadricyclic graphs was studied, and the corresponding extremal graphs were characterized.