Cartesian Products and Edge Domination

Abstract

A set of edges $D$ in a graph $G$ is a dominating set of edges if every edge not in $D$ is adjacent to at least one edge in $D$. The minimum cardinality of an edge dominating set of $G$ is the edge domination number of $G$, denoted by $D_E(G)$. In this paper, we investigate the edge domination number for the cartesian product of an $n$-colorable graph $G$ and the complete graph $K_n$.