2023/06/07 by Kirsti Kuenzel, Kuenzel, Kirsti, Douglas F. Rall +1
Computer Science · Mathematics · #05C69 #05C75 #05C76 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2306.04105
openalex publication_date 2023/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A graph is well-dominated if all its minimal dominating sets have the same cardinality. In this paper we prove that at least one factor of every connected, well-dominated Cartesian product is a complete graph, which then allows us to give a complete characterization of the connected, well-dominated Cartesian products if both factors have order at least 2. In particular, we show that G \Box H is well-dominated if and only if G \Box H = P3 \Box K3 or G \Box H= Kn \Box Kn for some n≥ 2.