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

• M, Nalliah ^[1]
  1. [1] Vellore Institute of Technology, Vellore
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 43, Nº. 2, 2024, págs. 473-494
• Idioma: inglés
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• Resumen

  • Let $G$ be a graph on $p$ vertices and $q$ edges with no isolated vertices. A bijection $f: V\rightarrow \{1,2,3,...,p\}$ is called local distance antimagic labeling, if for any two adjacent vertices $u$ and $v$, we have $w(u) \neq w(v)$, where $w(u)=\sum_{x\epsilon N(u)} {f(x)}$. The local distance antimagic chromatic number $\chi_{lda}(G)$ 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