On (k, d)-Hooked Skolem Graceful Graphs

By : S. Arumugam, Tarkeshwar Singh, Jessica Pereira

Page No: 7-15

Abstract
A (p, q) graphG = (V, E) is said to be (k, d)-hooked Skolem graceful if there exists a bijection f : V (G)? {1, 2, . . . , p ? 1, p + 1} such that the induced edge labeling gf : E ? {k, k + d, . . . , k + (q ? 1)d} defined by gf (uv)= |f (u)? f (v)|?uv ? E is also bijective, where k and d are positive integers. Such a labeling f is called (k, d)-hooked Skolem graceful labeling of G. Note that when k = d = 1, this notion coincides with that of hooked Skolem (HS) graceful labeling of the graph G. In this paper, we present some preliminary results on (k, d)-hooked Skolem graceful graphs and prove that nK2 is (2, 1)-hooked Skolem graceful if and only if n ? 1 or 2 (mod 4).

Authors :
Jessica Pereira and Tarkeshwar Singh : Department of Mathematics, Birla Institute of Technology and Science Pilani K K Birla, Goa Campus, NH-17B, Zuarinagar, Goa, India