An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it Bijection f : E ? {1, … ,|E|} such that for any pair adjacent vertices x and y, f+(x) ? f+(y), where the induced vertex label ?f(e), with e ranging over all edges incident x. The chromatic number G, denoted by ?la(G), minimum distinct labels labelings G. In this paper, we first show d-leg spider has d + 1 ? ?la...

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 local edge antimagic labeling if for any two adjacent edges e uv e’ vw G, we have w(e) ≠ w(e’), where the weight w(e uv) f(u)+f(v) w(e’) f(v)+f(w). has labeling. The chromatic number χ’lea(G) defined to minimum colors taken over all colorings induced by labelings G. In thi...