路径结构网络多层次距离标注的一种不同方法

IF 0.7 Q2 MATHEMATICS
L. Saha
{"title":"路径结构网络多层次距离标注的一种不同方法","authors":"L. Saha","doi":"10.5556/j.tkjm.55.2024.3913","DOIUrl":null,"url":null,"abstract":"For a positive integer $k$, a radio $k$-labelling of a simple connected graph $G=(V, E)$ is a mapping $f$ from the vertex set $V(G)$ to a set of non-negative integers such that $|f(u)-f(v)|\\geqslant k+1-d(u,v)$ for each pair of distinct vertices $u$ and $v$ of $G$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$. The \\emph{span} of a radio $k$-coloring $f$, denoted by $span_f(G)$, is defined as $\\displaystyle\\max_{v\\in V(G)}f(v)$ and the \\emph{radio $k$-chromatic number of $G$}, denoted by $rc_k(G)$, is $\\displaystyle\\min_{f}\\{~span_f(G)\\}$ where the minimum is taken over all radio $k$-labellings of $G$. In this article, we present results of radio $k$-chromatic number of path $P_n$ for $k\\in\\{n-1, n-2,n-3\\}$ in different approach but simple way.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"80 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A different approach for multi-level distance labellings of path structure networks\",\"authors\":\"L. Saha\",\"doi\":\"10.5556/j.tkjm.55.2024.3913\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a positive integer $k$, a radio $k$-labelling of a simple connected graph $G=(V, E)$ is a mapping $f$ from the vertex set $V(G)$ to a set of non-negative integers such that $|f(u)-f(v)|\\\\geqslant k+1-d(u,v)$ for each pair of distinct vertices $u$ and $v$ of $G$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$. The \\\\emph{span} of a radio $k$-coloring $f$, denoted by $span_f(G)$, is defined as $\\\\displaystyle\\\\max_{v\\\\in V(G)}f(v)$ and the \\\\emph{radio $k$-chromatic number of $G$}, denoted by $rc_k(G)$, is $\\\\displaystyle\\\\min_{f}\\\\{~span_f(G)\\\\}$ where the minimum is taken over all radio $k$-labellings of $G$. In this article, we present results of radio $k$-chromatic number of path $P_n$ for $k\\\\in\\\\{n-1, n-2,n-3\\\\}$ in different approach but simple way.\",\"PeriodicalId\":45776,\"journal\":{\"name\":\"Tamkang Journal of Mathematics\",\"volume\":\"80 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-03-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tamkang Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5556/j.tkjm.55.2024.3913\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/j.tkjm.55.2024.3913","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

对于正整数$k$,简单连通图$G=(V, E)$的无线$k$标记是将$f$从顶点集$V(G)$映射到一组非负整数,使得$|f(u)-f(v)|\geqslant k+1-d(u,v)$对应$G$的每一对不同的顶点$u$和$v$,其中$d(u,v)$是$G$中$u$和$v$之间的距离。$k$ -着色$f$的无线电\emph{跨度}(表示$span_f(G)$)定义为$\displaystyle\max_{v\in V(G)}f(v)$, \emph{$G$}\emph{的}\emph{无线电}\emph{$k$}\emph{-色数}(表示$rc_k(G)$)定义为$\displaystyle\min_{f}\{~span_f(G)\}$,其中最小值取$G$的所有无线电$k$ -标签。在本文中,我们以不同的方法但简单的方法给出了$k\in\{n-1, n-2,n-3\}$的无线电$k$ -路径$P_n$的色数的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A different approach for multi-level distance labellings of path structure networks
For a positive integer $k$, a radio $k$-labelling of a simple connected graph $G=(V, E)$ is a mapping $f$ from the vertex set $V(G)$ to a set of non-negative integers such that $|f(u)-f(v)|\geqslant k+1-d(u,v)$ for each pair of distinct vertices $u$ and $v$ of $G$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$. The \emph{span} of a radio $k$-coloring $f$, denoted by $span_f(G)$, is defined as $\displaystyle\max_{v\in V(G)}f(v)$ and the \emph{radio $k$-chromatic number of $G$}, denoted by $rc_k(G)$, is $\displaystyle\min_{f}\{~span_f(G)\}$ where the minimum is taken over all radio $k$-labellings of $G$. In this article, we present results of radio $k$-chromatic number of path $P_n$ for $k\in\{n-1, n-2,n-3\}$ in different approach but simple way.
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
1.50
自引率
0.00%
发文量
11
期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
×
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