The maximum Laplacian separators of bicyclic and tricyclic graphs

Let G be an undirected simple graph of order n, L(G) be the Laplacian matrix of G, and μ1(G)≥μ2(G) ≥…≥μn(G) be the eigenvalues of L(G). The Laplacian separator of G is defined as SL(G)=μ1(G)-μ2(G). Here the maximum Laplacian separators of bicyclic and tricyclic graphs of a given order were studied, and the corresponding extremal graphs were characterized.