Local Total Antimagic Chromatic Number for the Disjoint Union of Star Graphs

Let G be a graph with n vertices and m edges without isolated vertices. A local total antimagic labeling of a graph G is defined as there is a bijection f from the set V(G) boolean OR E ( G ) -> {1, 2, ..., n + m }, such that, any two adjacent vertices, any two adjacent edges, a vertex and an edge incident to the vertex does not receive the same weight. The vertex weight is the sum of the edge labels incident to that vertex and the edge weight is the sum of its end vertex labels. The local total antimagic chromatic number is the minimum number of colors taken over all induced by local total antimagic colorings (labelings) of G, which is denoted by chi lt ( G ). In this paper, we determine the local total antimagic chromatic number for the disjoint union of star graphs.