Skolem Graceful Signed Stars

Abstract

In this paper, we obtain a necessary condition for the Skolem gracefulness of the disjoint union of $k$ signed stars $K_{1,r_i},1\le i\le k$, which we call a $k$-signed star $St(r_1,r_2,\dots ,r_k)$. We also present results on the Skolem gracefulness of the 2-signed star $St(r_1,r_2)$.