Abstract: Let denote a random graph obtained from a complete labelled graph on
vertices by independent deletion of its edges with the prescribed probability
Moreover, let and let denote the number of
-vertex subgraphs of a random graph being -trees. In
this paper we prove that, under some conditions imposed on probability as
the random variable has asymptotically the Poisson or normal
distribution. We generalize earlier results of Erdös and Rényi [2] dealing with the
distribution of the number of trees (i.e. random variable as well as the results of
Schürger [7] on the number of cliques in (i.e. random variable