We also determined the local distance antimagic chromatic number of join products of some graphs with cycles or paths.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $G$ be a graph of order $p$ without isolated vertices.
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Key Findings & Data: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 $w_f(u)=\sum_{x\epsilon N(u)} {f(x)}$.
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Conclusion & Impact:We also determined the local distance antimagic chromatic number of join products of some graphs with cycles or paths.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:local distance antimagic chromatic number · join product · cycle
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.
Shiu, W., Lau, G., M, N. (2024). Local distance antimagic cromatic number of join product of graphs with cycles or paths. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 3. https://doi.org/10.15672/hujms.1266085
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