  This paper investigates some relationship between the algebraic connectivity
and the clique number of graphs. We characterize all extremal graphs which have
the maximum and minimum the algebraic connectivity among all graphs of order
$n$ with the clique number $r$, respectively. In turn, an upper and lower
bounds for the clique number of a graph in terms of the algebraic connectivity
are obtained. Moreover, a spectral version of the Erd\H{o}s-Stone theorem in
terms of the algebraic connectivity of graphs is presented.

Combinatorics