On the vertex local antimagic total labeling chromatic number of $G\odot {K}_{2}$
Elsa Yuli Kurniawati, Ika Hesti Agustin, Dafik Dafik, Marsidi Marsidi · Journal of Physics Conference Series · 2019
A graph G ( V, E ) consists vertices and edges. As usual, the vertex set denoted by V and edge set by E . The concept of local antimagic coloring of a graph was introduced by Arumugam et.al . Thus, we study the concept of local antimagic namely vertex local antimagic total labeling. Vertex local antimagic total labeling is defined if for any two adjacent vertex v 1 and v 2 , , 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, the local antimagic total labeling induces a proper vertex coloring of G if each vertex v is assigned the color w t ( v ). The vertex local antimagic total labeling chromatic number of graph G denoted by X latv ( G ). In this paper we study the local antimagic total vertex coloring of graph and determined exact value of graphs as follows and .