On local antimagic vertex coloring of corona products related to friendship and fan graph

Abstract

Let G=(V,E) be connected graph. A bijection f : E → {1,2,3,..., |E|} is a local antimagic of G if any adjacent vertices u,v ∈ V satisfies w(u)≠ w(v), where w(u)=∑_e∈E(u) f(e), E(u) is the set of edges incident to u. When vertex u is assigned the color w(u), we called it a local antimagic vertex coloring of G. A local antimagic chromatic number of G, denoted by χ_la(G), is the minimum number of colors taken over all colorings induced by the local antimagic labeling of G. In this paper, we determine the local antimagic chromatic number of corona product of friendship and fan with null graph on m vertices, namely, χ_la(F_n ⊙ \overline{K_m}) and χ_la(f_(1,n) ⊙ \overline{K_m}).