On the limit distribution of the number of cycles in a random graph

Let Γ n ( p ) denote a random graph with n vertices in which any two vertices, independently of the others, are connected by an edge with probability p where . Denote by γ n ( p ) the total number of cycles in the graph Γ n ( p ). The main object of this paper is to prove that the limit distribution of γ n ( λ /n ) is a Poisson distribution with expectation if n → ∞and 0 < λ< 1.