An algebraic approach to sets defining minimal dominating sets of regular graphs - Mehrdad Nasernejad (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2023)
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.