Local antimagic vertex total coloring on fan graph and graph resulting from comb product operation

Let G = (V,E) be a connected graph with |V|=n and |E|=m. A bijection f: V(G) U E(G) → {1,2,3, …,n + m} is called local antimagic vertex total coloring if for any two adjacent vertices u and v, w t (u) ≠ w t (v), where w t (u) = ∑ e∈E(u) f(e) + f(u), and E (u) is a set of edges incident to u. Thus any local antimagic vertex total labeling induces a proper vertex coloring of G where the vertex v is assigned the color w t (v). The local antimagic vertex total chromatic number χ 1να t (G) is the minimum number of colors taken over all colorings induced by local antimagic vertex total. In this paper we investigate local antimagic vertex total coloring on fan graph (F n ) and graph resulting from comb product operation of F n and F 3 which denoted by F n t> F 3 . We get two theorems related to the local antimagic vertex total chromatic number. First, χ 1να t (F n ) = 3 where n> 3. Second, 3 F 3 ) 3.