A sharp upper bound of the spectral radius of graphs

Let G be a simple connected graph with n vertices and m edges. Let S(G) = S br the minimum degree of vertices of G. Thr spectral radius p(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we obtain the following sharp upper bound of p(G): [GRAPHICS] Equality holds if and only if G is either a regular graph or a bidegreed graph in which each vertex is of degree either S or n - 1. (C) 2001 Academic Press.