A characterization of well-dominated Cartesian products

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 (sic) His well-dominated if and only if G (sic) H= P-3 (sic) K(3)or G (sic) H= K-n (sic) K-n for some n >= 2. (c) 2024 Elsevier B.V. All rights reserved.