On local distance antimagic chromatic number of graphs disjoint union with 1-regular graphs

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) w (v), where w (u) =ₗ ₍ (ₔ) f (x). The local distance antimagic chromatic number ₋₃₀ (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 obtained the necessary and sufficient condition for the local distance antimagic chromatic number of some disjoint union of graphs with 1-regular graphs equal to the number of distinct neighbors of its pendant vertices. We also gave a correct result in Local Distance Antimagic Vertex Coloring of Graphs, https: //arxiv. org/abs/2106. 01833v1 (2021). %magic Vertex Coloring of Graphs, https: //arxiv. org/abs/2106. 01833v1