Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 7 2 2022 09 01 On Clique Mantel's Theorem 171 178 326 10.22128/gadm.2022.630.1084 EN Hossein Teimoori Faal Department of Mathematics and Computer Science, Allameh Tabataba’i University, Tehran, Iran Journal Article 2022 11 30 A complete subgraph of any simple graph <em>G</em> on <em>k</em> vertices is called a <em>k-clique</em> of <em>G</em>. In this paper, we first introduce the concept of the value of a <em>k-clique (k>1)</em> as an extension of the idea of the degree of a given vertex. Then, we obtain <br />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 <em>n</em> vertices is equal to n²/4. Our main goal here is to find an extension of the above result for the class of <em>K_ω+1</em>-free graphs, using the ideas of the value of cliques and the clique handshaking lemma. https://ansne.du.ac.ir/article_326_7bc8a3ae1e7f8e50e11f41b038cce1c4.pdf