{"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}
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.
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.