On Clique Mantel's Theorem

Document Type : Research Paper


Department of Mathematics and Computer Science, Allameh Tabataba’i University, Tehran, Iran


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.