A note on Laplacian graph eigenvalues

Abstract

Let G = (V, E) be a graph on n vertices. Denote by d(v) the degree of v ∈ 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 ∈ 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. © 1998 Elsevier Science Inc. All rights reserved.