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Abstract
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Suppose that V = {1, . . . , n} is a non-empty set of n elements, S = {S1, . . . , Sm} a non-empty family of m non-empty subsets of V . In this paper, by using some algebraic notions in commutative algebra, we investigate the question arises whether there exists an undirected finite simple graph G with V (G) = V where S is the set whose elements are the minimal dominating sets of G.
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