Domination versus edge domination (Q2197443)

In this paper, the authors establish a conjecture about the relationship of domination number and edge domination number of a $\Delta$-regular graph $G$ with $\Delta\geq 1$. Moreover, they obtain three results related to this conjecture where $G$ is a $\Delta$-regular graph with $\Delta\geq 1$, $G$ is a cubic graph and $G$ is a cubic claw-free graph, respectively.