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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Mehrdad Nasernejad
Univ. Artois, UR 2462, Laboratoire de Mathematique de Lens (LML), F-62300 Lens, France.
Electrical & Electronics Engineering

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An algebraic approach to sets defining minimal dominating sets of regular graphs Mehrdad Nasernejad
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.5

Abstract

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.
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