On a conjecture of V. Nikiforov

In this paper we will prove that μ ( G ) + μ ( G ¯ ) ≤ 1 + 3 2 n − 1 . where μ ( G ) , μ ( G ¯ ) are the greatest eigenvalues of the adjacency matrices of the graph G and its complement and n denotes the number of vertices of G .