On the Edge-Graceful $(n,kn)$ -Multigraphs Conjecture

Abstract

Lee conjectures that for any $k>1$, a $(n,nk)$-multigraph decomposable into $k$ Hamiltonian cycles is edge-graceful if $n$ is odd. We investigate the edge-gracefulness of a special class of regular multigraphs and show that the conjecture is true for this class of multigraphs.