A note on the bounds for the spectral radius of graphs

Abstract

Let G=(V,E) be a finite undirected graph of order n and of size m. Let Δ and δ be the largest and the smallest degree of G, respectively. The spectral radius of G is the largest eigenvalue of the adjacency matrix of the graph G. In this note we give new bounds on the spectral radius of {C3,C4}-free graphs in terms of m,n,Δ and δ. Computer search shows that in most of the cases the bounds derived in this note are better than the existing bounds.