On local edge antimagic chromatic number of graphs

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called a local edge antimagic labeling if for any two adjacent edges e = uv and e’ = vw of G, we have w(e) ≠ w(e’), where the edge weight w(e = uv) = f(u)+f(v) and w(e’) = f(v)+f(w). A graph G is local edge antimagic if G has a local edge antimagic labeling. The local edge antimagic chromatic number χ’lea(G) is defined to be the minimum number of colors taken over all colorings of G induced by local edge antimagic labelings of G. In this paper, we determine the local edge antimagic chromatic number for a friendship graph, wheel graph, fan graph, helm graph, flower graph, and closed helm.