{"title":"Local antimagic chromatic number for the corona product of wheel and null graphs","authors":"Rathinavel Shankar, M. Nalliah","doi":"10.35634/vm220308","DOIUrl":null,"url":null,"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.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35634/vm220308","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.