{"title":"轮图与零图的电晕积的局部反幻色数","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":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":43239,\"journal\":{\"name\":\"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35634/vm220308\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35634/vm220308","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Local antimagic chromatic number for the corona product of wheel and null graphs
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.