On edge graceful labelings of disjoint unions of $2r$-regular edge   graceful graphs
  We prove that if $G$ is a $2r$-regular edge graceful $(p,q)$ graph with $(r,kp)=1$ then $kG$ is edge graceful for odd $k$. We also prove that for certain specific classes of $2r$-regular edge graceful graphs it is possible to drop the requirement that $(r,kp)=1$ 
Adrian Riskin and Georgia Weidman