Product Edge-Antimagic Vertex Labeling of Graphs

Abstract

A (p, q)-graph G, is defined to be product antimagic if there is a labeling from E(G) onto
{1, 2, . . . , q} such that, at each vertex u, the product of the labels on the edges incident with u are distinct. Similarly, a (p, q)-graph G is defined to be product edge-antimagic if there is a labeling f from onto {1, 2, . . . , p + q} with the property that the value , for any edge  are distinct. In this paper, we introduce the product edge-antimagic vertex (PEAV) labeling as a bijection f from V(G) to
{1, 2, . . . , p} such that, for any edge , the product  are distinct. Also we have proved the existence of PEAV labeling for paths and cycles.