Minimal Dominating Sets of Regular Graphs through the Lens of Monomial Ideals

par Mehrdad Nasernejad

mardi 1 déc. 2026, 14:00 → 15:30 Europe/Paris

S3 351 (Sciences 3)

Suppose V = {1, . . . , n} is a non-empty set of n elements, S = {S₁, . . . , S_m} a non-empty set of m non-empty subsets of V . In this talk, 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.

Source : M. Nasernejad, An algebraic approach to sets defining minimal dominating sets of regular graphs, Electron. J. Graph Theory Appl. (EJGTA) 11 (2023), no. 2, 401–409.
doi : https://dx.doi.org/10.5614/ejgta.2023.11.2.5