On unique minimum dominating sets in some Cartesian product graphs
Jason T. Hedetniemi · Discussiones Mathematicae Graph Theory · 2015
Unique minimum vertex dominating sets in the Cartesian product of a graph with a complete graph are considered.We first give properties of such sets when they exist.We then show that when the first factor of the product is a tree, consideration of the tree alone is sufficient to determine if the product has a unique minimum dominating set.