Distance antimagic labelings of Cartesian product of graphs

Abstract

Let be a graph of order n. Let be a bijection. The weight w(v) of a vertex v with respect to the labeling f is defined by where N(v) is the open neighborhood of v. The labeling f is called a distance antimagic labeling if for any two distinct vertices v1, v2 in V. In this paper we investigate the existence of distance antimagic labeling for the Cartesian product where the graphs G and H are cycles or complete graphs.