The Laplacian spectral radius of graphs on surfaces Original Research Article

Let G be an n-vertex (ngreater-or-equal, slanted3) simple graph embeddable on a surface of Euler genus γ (the number of crosscaps plus twice the number of handles). Denote by Δ the maximum degree of G. In this paper, we first present two upper bounds on the Laplacian spectral radius of G as follows: (i) image (ii) if G is 4-connected and either the surface is the sphere or the embedding is 4-representative, thenimage Some upper bounds on the Laplacian spectral radius of the outerplanar and Halin graphs are also given.