R. Merris, A note on Laplacian graph eigenvalues, Linear Algebra Appl. 285 (1998), 33-35. Math Reviews 2000a:05143.


Let G be a graph. Denote by d(v) the degree of vertex v of G and by m(v) the average of the degrees of the vertices of G adjacent to v. The main result of this note is that the maximum, over v, of d(v) + m(v) is an upper bound for the Laplacian spectral radius of G.


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