In this paper, we give a necessary condition for an odd degree graph to be Skolem-graceful and we prove that if \(G\) is a \((p, q)\) pseudograceful graph such that \(p=q+tl\), then \(G\cup S_m\) is Skolem-graceful for all \(m\geq 1\). Finally, we give some variations on the definition of cordial graphs.