On Unique Minimum Dominating Sets in Some Cartesian Product Graphs

Abstract

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.

Keywords

• vertex domination
• graph products
• trees