Local antimagic vertex coloring for generalized friendship graphs

Abstract

Let G = (V, E) be a graph of order p and size q without isolated vertices. A bijection f: E → {1, 2, … , q} is called a local antimagic labeling if w(u) ≠ w(v) for all uv ∈ E, where the vertex weight w(u) = Ʃ e∈E(u) f(e) and E(u) is the set of edges incident to the vertex u ∈ V. The local antimagic chromatic number χ la (G) is defined to be the minimum number of colors(vertex weights) taken over all colorings of G induced by local antimagic labelings of G. In this paper, we study the local chromatic number for generalized friendship graph of complete graphs and cycles.