On edge graceful labelings of disjoint unions of $2r$-regular edge graceful graphs

Riskin, Adrian; Weidman, Georgia

On edge graceful labelings of disjoint unions of $2r$-regular edge graceful graphs

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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 $(r,kp)=1$