On Clique Mantel's Theorem

A complete subgraph of any simple graph G on k vertices is called a k-clique of G. In this paper, we first introduce the concept of the value of a k-clique (k>۱) as an extension of the idea of the degree of a given vertex. Then, we obtain the generalized version of handshaking lemma which we call it clique handshaking lemma. The well-known classical result of Mantel states that the maximum number of edges in the class of triangle-free graphs with n vertices is equal to n۲/۴. Our main goal here is to find an extension of the above result for the class of Kω+۱-free graphs, using the ideas of the value of cliques and the clique handshaking lemma.