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 Gβ‘H is well-dominated if and only if Gβ‘H=P3ββ‘K3β or Gβ‘H=Knββ‘Knβ for some nβ₯2.Comment: 17 page