On the local vertex antimagic total coloring of some families tree

Abstract

Let G(V, E) be a graph of vertex set V and edge set E. Local vertex antimagic total coloring developed from local edge and local vertex antimagic coloring of graph. Local vertex antimagic total coloring is defined if for any two adjacent vertices v1 and v2, , where for , where E(v) and V(v) are respectively the set of edges incident to v and the set of vertices adjacent to v. Thus, any local vertex antimagic total coloring induces a proper vertex coloring of G if each vertex v is assigned the color w(v). The chromatic number of local vertex antimagic total coloring denote χlvat(G) is the minimum number of colors taken over all colorings induced by local vertex antimagic total coloring of graph G. In this paper, we use some families tree graph. We also study the existence of local vertex antimagic total coloring chromatic number of some families tree namely star graph, double star graph, banana tree graph, centipede graph, and amalgamation of star graph.