On the study of local antimagic vertex coloring of graphs and their operations

Abstract

Arumugam paper studied in et al [4] has inspired us to study the same thing, namely local antimagic edge labeling of graphs. In this paper, we continue to study this type of coloring of some graphs and its operations. By a local antimagic edge labeling, we mean a bijection f from the edge set of G to the natural number up to the number of edges in G such that for any two adjacent vertices v and v’ have different weight, w(v) = w(v’), where w(v) = Σe∈E(v) f (e), and E(v) is the set of vertices which is incident to v. Furthermore, the vertex weight w(v) is assigned as the color on a vertex of G. The local antimagic chromatic number χ1α (G) is the minimum number of colors taken over all coloring induced by vertex local antimagic edge labeling of G.