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 \(K_n\).