  A complete subgraph of any simple graph $G$ on $k$ vertices is called a
$k$-\emph{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 $\frac{n^{2}}{4}$. Our main goal here is
to find an extension of the above result for the class of $K_{\omega+1}$-free
graphs, using the ideas of the value of cliques and the clique handshaking
lemma.
