Local antimagic chromatic number for the corona product of wheel and null graphs

Pub Date : 2022-09-01 DOI:10.35634/vm220308
Rathinavel Shankar, M. Nalliah
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Abstract

Let $G=(V,E)$ be a graph of order $p$ and size $q$ having no isolated vertices. A bijection $f\colon E\hm{\rightarrow}\left\{1,2,3,\ldots,q \right\}$ is called a local antimagic labeling if for all $uv\in E$, we have $w(u)\neq w(v)$, the weight $w(u)=\sum_{e\in E(u)}f(e)$, where $E(u)$ is the set of edges incident to $u$. A graph $G$ is local antimagic, if $G$ has a local antimagic labeling. The local antimagic chromatic number $\chi_{la}(G)$ is defined to be the minimum number of colors taken over all colorings of $G$ induced by local antimagic labelings of $G$. In this paper, we completely determine the local antimagic chromatic number for the corona product of wheel and null graphs.
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轮图与零图的电晕积的局部反幻色数
设$G=(V,E)$为阶为$p$,大小为$q$的图,没有孤立的顶点。双射$f\colon E\hm{\rightarrow}\left\{1,2,3,\ldots,q \right\}$被称为局部反魔术标记如果对于所有的$uv\in E$,我们有$w(u)\neq w(v)$,权值$w(u)=\sum_{e\in E(u)}f(e)$,其中$E(u)$是与$u$相关的边的集合。一个图$G$是局部反魔术,如果$G$有一个局部反魔术标记。局部反幻色数$\chi_{la}(G)$定义为由$G$的局部反幻标记诱导的$G$的所有着色所占的最小颜色数。本文完全确定了轮盘图与零图的电晕积的局部反幻色数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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