A bound on the spectral radius of graphs (Q1109050)

Let G be a simple connected graph with n vertices and m edges. Let A be the adjacency matrix of G. The spectral radius \(\rho\) (A) of A satisfies \(\rho (A)\leq \sqrt{2m-n+1}\) with equality if and only if G is isomorphic to one of the following two graphs: (a) star \(K_{1,n-1}\); (b) the complete graph \(K_ n\).