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

Mehrdad Nasernejad


Suppose that V = {1, …, n} is a non-empty set of n elements, S = {S1, …, Sm} 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.


minimal dominating sets, regular graphs, closed neighborhood ideals, dominating ideals

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