摘要

An (n, m)-graph is referred to be a graph with n vertices and m edges. Let Delta(G) and delta(G) be the maximum and minimum degree of a graph G and let mu(G) and q(G) be the Laplacian and signless Laplacian spectral radius of G, respectively. In this paper, we prove that for two connected nonregular (n,m)-graphs G and G', if Delta(G) >= 2m-(n-1) delta(G')/delta(G')+1 + delta (g') and Delta (G) > Delta(G') + delta(G') -1, then mu(G) > mu(G') and q(G) > q(G') . Also, we obtain that for two connected non-regular (n,m)-graphs G and G', if Delta (G) >= 2m-(n-1)delta(G')/delta(G')+1 + 1 and Delta(G) > Delta(G') then mu(G) > mu(G') - delta(G') + 1 and q(G) > q(G') - delta(G') + 1.