A generalization of a Turán's theorem about maximum clique on graphs.

One of the most important Turán's theorems establishes an inequality between the maximum clique and the number of edges of a graph. Since 1941, this result has received much attention and many of the different proofs involve induction and a probability distribution. In this paper we detail finite procedures that gives a proof for the Turán's Theorem. Among other things, we give a generalization of this result. Also we apply this results to a Nikiforov's inequality between the spectral radius and the maximum clique of a graph. [ABSTRACT FROM AUTHOR]