{"title":"Weak Signed Roman Domination in Digraphs","authors":"L. Volkmann","doi":"10.5556/J.TKJM.52.2021.3523","DOIUrl":null,"url":null,"abstract":"Let $D$ be a finite and simple digraph with vertex set $V(D)$. A weak signed Roman dominating function (WSRDF) on a digraph $D$ is a function $f:V(D)\\rightarrow\\{-1,1,2\\}$ satisfying the condition that $\\sum_{x\\in N^-[v]}f(x)\\ge 1$ for each $v\\in V(D)$, where $N^-[v]$ consists of $v$ and allvertices of $D$ from which arcs go into $v$. The weight of a WSRDF $f$ is $\\sum_{v\\in V(D)}f(v)$. The weak signed Roman domination number $\\gamma_{wsR}(D)$ of $D$ is the minimum weight of a WSRDF on $D$. In this paper we initiate the study of the weak signed Roman domination number of digraphs, and we present different bounds on $\\gamma_{wsR}(D)$. In addition, we determine the weak signed Roman domination number of some classesof digraphs.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/J.TKJM.52.2021.3523","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: 1
Abstract
Let $D$ be a finite and simple digraph with vertex set $V(D)$. A weak signed Roman dominating function (WSRDF) on a digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2\}$ satisfying the condition that $\sum_{x\in N^-[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ consists of $v$ and allvertices of $D$ from which arcs go into $v$. The weight of a WSRDF $f$ is $\sum_{v\in V(D)}f(v)$. The weak signed Roman domination number $\gamma_{wsR}(D)$ of $D$ is the minimum weight of a WSRDF on $D$. In this paper we initiate the study of the weak signed Roman domination number of digraphs, and we present different bounds on $\gamma_{wsR}(D)$. In addition, we determine the weak signed Roman domination number of some classesof digraphs.
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.