SEPARATING SETS AND LAPLACIAN EIGENVALUES OF GRAPHS

Let G be a graph of order n and 0 = µ 1 (G) ≤ µ 2 (G) ≤ · · · ≤ µ n (G) be the Laplacian eigenvalues of G. Haemers [1] proved that: If X and Y are two disjoint sets of vertices of G such that there is no edge between X and Y , then | X || Y | (n − | X | )(n − | Y | ) ≤ ( LS(G) µ n (G) + µ 2 (G) ) 2 . In this talk we would like to generalize this result whenever the edges between X and Y form a bipartite regular graph.