Local distance antimagic cromatic number of join product of graphs with cycles or paths

Year 2024, Volume: 53 Issue: 3, 788 - 802, 27.06.2024

Wai-chee Shiu Gee-choon Lau Nalliah M

https://doi.org/10.15672/hujms.1266085

Abstract

Let $G$ be a graph of order $p$ without isolated vertices. A bijection $f: V \to \{1,2,3,\dots,p\}$ is called a local distance antimagic labeling, if $w_f(u)\ne w_f(v)$ for every edge $uv$ of $G$, where $w_f(u)=\sum_{x\epsilon N(u)} {f(x)}$. 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 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.

Keywords

local distance antimagic chromatic number, join product, cycle, path, null graph

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