On the spectral radius of graphs

Let <f>G</f> be a simple undirected graph. For <f>v∈V(G)</f>, the 2-degree of <f>v</f> is the sum of the degrees of the vertices adjacent to <f>v</f>. Denote by <f>ρ(G)</f> and <f>μ(G)</f> the spectral radius of the adjacency matrix and the Laplacian matrix of <f>G</f>, respectively. In this paper, we present two lower bounds of <f>ρ(G)</f> and <f>μ(G)</f> in terms of the degrees and the 2-degrees of vertices. [Copyright &y& Elsevier]