Local distance antimagic chromatic number for the union of complete bipartite graphs

Abstract

Let G be a graph on p vertices and q edges with no isolated vertices. A bijection f : V → {1, 2, 3, ..., p} is called local distance antimagic labeling, if for any two adjacent vertices u and v, we have w(u) is not equal to w(v), where w(u) is the sum of all neighbour labels of u. The local distance antimagic chromatic number χlda(G) is defined to be the minimum number of colors taken overall colorings of G induced by local distance antimagic labelings of G. In this paper, we determine the graph G for the local distance antimagic chromatic number is 2.