An algebraic approach to sets defining minimal dominating sets of regular graphs

Abstract

Suppose that V = {1, …, n } is a non-empty set of n elements, S = { S 1 , …, S m } a non-empty set 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 .