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>1) 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 n2/4. our main goal here is to find an extension of the above result for the class of kω+1-free graphs, using the ideas of the value of cliques and the clique handshaking lemma.