A note on Laplacian graph eigenvalues Original Research Article

Let G = (V,E) be a graph on n vertices. Denote by d(v) the degree of v set membership, variant V and by m(v) the average of the degrees of the vertices of G adjacent to v. Then b(G) = max{m(v) + d(v): v set membership, variant V} is an upper bound for the Laplacian spectral radius of G; hence, n − b(GC) is a lower bound for the algebraic connectivity of G in terms of the vertex degrees of its complement.