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Let G n,d be a random d-regular graph with n vertices. Given a fixed graph H. W denotes the number of induced copies of H in G n,d . In this paper, we use Stein-Chen method and Local approach to show that W can approximate by the Poisson distribution and give the bound of this approximation.

In this paper, we introduce the iterative scheme for finding a common fixed point of a countable family of G-nonexpansive mappings by the shrinking projection method which generalizes Takahashi Takeuchi and Kubota’s theorem in a Hilbert space with a directed graph. Simultaneously, we give examples and numerical results for supporting our main theorems and compare the rate of convergence of some examples under the same conditions.

Let W be the number of copies of a fixed graph H in a random dregular graph G n,d . In this paper, we give the bound on Poisson approximation of W by using the Stein-Chen method.

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