LOCAL EDGE ANTIMAGIC COLORING OF GRAPHS

Abstract

All graphs considered in this paper are finite, simple and connected graphs. Let G(V, E) be a graph with the vertex set V and the edge set E, and let w be the edge weight of graph G. Then a bijection f: V (G) → {1, 2, 3, …, |V (G)|} is called a local edge labeling if for adjacent edges e1 and e2, w(e1) ≠ w(e2), where for e = uv ∈ G, w(e) = f (u) + f (v). It is known that any local edge antimagic labeling induces a proper edge coloring of G if each edge e is assigned the color w(e). The local edge antimagic chromatic number γlea(G) is the minimum number of colors taken over all colorings induced by local edge antimagic labelings of G. In this paper, we initiate to study the existence of local edge antimagic coloring of some special graphs. We also analyse the lower bound of its local edge antimagic chromatic number.