Local Distance Antimagic Chromatic Number of Join Product of Graphs with Cycles or Paths

Abstract

Let G be a graph of order p without isolated vertices. A bijection f : V → {1, 2, 3, . . . , p} is called a local distance antimagic labeling, if wf (u) ̸= wf (v) for every edge uv of G, where wf(u) =ΣxϵN(u) f(x). The local distance antimagic chromatic number χlda(G) is defined to be the minimum number of colors taken over all colorings of G induced by local distance antimagic labelings of G. In this paper, we determined the local distance antimagic chromatic number of some cycles, paths, disjoint union of 3-paths. We also determined the local distance antimagic chromatic number of join products of some graphs with cycles or paths.