Edge domination in graphs

Abstract

Let $G$ be a $(p,q)$-graph with edge domination number $\gamma '$ and edge domatic number $d'$. In this paper we characterize connected graphs for which $\gamma ' = p/2$ and graphs for which $\gamma ' + d' = q + 1$. We also characterize trees and unicyclic graphs for which $\gamma ' = \lfloor p/2 \rfloor $ and $\gamma ' = q - \Delta '$, where $\Delta '$ denotes the maximum degree of an edge in $G$.