On the Edge-graceful Spectra of the Cylinder Graphs (I)
Sin-Min Lee, Claude Lévesque, Karl Schaffer · 2008
Abstract. Let G be a (p,q)-graph and k~O. A graph G is said to be k-edgegraceful if the edges can be labeled by k,k+I,...,k+q-I so that the vertex sums are distinct, modulo p. We denote the set of all k such that G is k-edge graceful by egS(G). The set is called the edge-graceful spectrum ofG. In this paper, we are concerned with the problem of exhibiting sets of natural numbers which are the edge-graceful spectra of the cylinder CnxPm for certain values of n and m. 1. Introduction. Given an integer kEN = {l,2,3,...}, a graph G = (V, E) with p vertices and q edges is said to be k- edge-graceful ifthere is a bijection f: E-{k,k+I,k+2,...,k+q-I} such that the induced mapping r+:V-Zp, given by