Publications

Abstract : Let G = (V, E) be a connected graph with |V| = n and | E| = m. A bijection f from E to the set of integers {1,2,…, m} is called a local antimagic labeling of G if for any two adjacent vertices u and v in G, w(u) is not equal to w(v), where w (u) is the sum of the labels of all the edges incident to u. Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color w ( v ). Also, the local antimagic chromatic number is defined to be the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this paper, the local antimagic chromatic number of diameter 3 trees, certain classes of diameter 4 trees and complete bipartite graph K m,n where m and n are of different parity are obtained.