Local Edge Antimagic Coloring of Comb Product of Graphs

Abstract

All graph in this paper are ¯nite, simple and connected graph. Let G(V; E) be a graph of vertex set V and edge set E. A bijection f : V (G) ¡! f1; 2; 3; :::; jV (G)jg is called a local edge antimagic labeling if for any two adjacent edges e 1 and e 2 , w(e 1 ) 6 = w(e ), where for e = uv 2 G, w(e) = f(u) + f(v). Thus, 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 hromatic number ° 2 (G) is the minimum number of colors taken over all colorings induced by local edge antimagic labelings of G. In this paper, we have found the lower bound of the local edge antimagic coloring of G . H and determine exact value local edge antimagic coloring of G . H.