轮图与零图的电晕积的局部反幻色数

IF 0.6 Q3 MATHEMATICS
Rathinavel Shankar, M. Nalliah
{"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}
引用次数: 0

摘要

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。
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.20
自引率
40.00%
发文量
27
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信