On (k, d)-Skolem Graceful Graphs

A graph G=(V,E) is said to be (k, d)-Skolem graceful if there exists a bijection f:V(G)→{1,2,…,|V|} such that the induced edge labeling gf defined by gf(uv)=|f(u)−f(v)| is a bijection from E to {k,k+d,…,k+(q−1)d} where k and d are positive integers. Such a labeling f is called a (k, d)-Skolem graceful labeling of G. In this paper, we present a few basic results on (k, d)-Skolem graceful graphs. We prove that nK2 is (2, 1)-Skolem graceful if and only if , which produces the Langford sequence L(2,n).