Let X be a non-empty set and R be the power set of X. Then (R;Δ; ^) is a commutative ring with an identity element, where Δ is the symmetric difference. For a natural number n, R is a graph with vertex set R^n-0 and two distinct vertices Y and Z are adjacent if and only if there exists a lower triangular matrix A over R such that, for each iA_i,i\= 0 and also AY = Z or AZ = Y. In this paper we show that if |X|> 2, for each natural number n, the graph G_n R has a Hamiltonian cycle except the case that |X|= 2 and n = 1. Also we investigate the clique number of G_n R. Moreover we obtain a suitable bound for the independence number of G_n R.

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