Local vertex antimagic chromatic number of some wheel related graphs

Abstract

Let G = (V,E) be a graph of order p and size q having no isolated vertices. A bijection ƒ : E → {1, 2, 3, ..., q} is called a local antimagic labeling if for all uv ∈ E we have w(u) ≠ w(v), the weight w(u) = ∑e∈E(u) f(e) where E(u) is the set of edges incident to u. A graph G is local antimagic if G has a local antimagic labeling. The local antimagic chromatic number χla(G) is defined to be the minimum number of colors taken over all colorings of G induced by local antimagic labelings of G. In this paper, we determine the local antimagic chromatic number for some wheel related graphs.