{"title":"On the signed strong total Roman domination number of graphs","authors":"A. Mahmoodi, M. Atapour, S. Norouzian","doi":"10.5556/j.tkjm.54.2023.3907","DOIUrl":null,"url":null,"abstract":"Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $\\Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)\\rightarrow\\{-1, 1,2,\\ldots, \\lceil\\frac{\\Delta}{2}\\rceil+1\\}$ satisfying the condition that (i) forevery vertex $v$ of $G$, $f(N(v))=\\sum_{u\\in N(v)}f(u)\\geq 1$, where$N(v)$ is the open neighborhood of $v$ and (ii) every vertex $v$ forwhich $f(v)=-1$ is adjacent to at least one vertex$w$ for which $f(w)\\geq 1+\\lceil\\frac{1}{2}\\vert N(w)\\cap V_{-1}\\vert\\rceil$, where$V_{-1}=\\{v\\in V: f(v)=-1\\}$.The minimum of thevalues $\\omega(f)=\\sum_{v\\in V}f(v)$, taken over all signed strongtotal Roman dominating functions $f$ of $G$, is called the signed strong totalRoman domination number of $G$ and is denoted by $\\gamma_{ssTR}(G)$.In this paper, we initiate signed strong total Roman domination number of a graph and giveseveral bounds for this parameter. Then, among other results, we determine the signed strong total Roman dominationnumber of special classes of graphs.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-07-29","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.54.2023.3907","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
Abstract
Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximumdegree $\Delta$. A signed strong total Roman dominating function ona graph $G$ is a function $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil\frac{\Delta}{2}\rceil+1\}$ satisfying the condition that (i) forevery vertex $v$ of $G$, $f(N(v))=\sum_{u\in N(v)}f(u)\geq 1$, where$N(v)$ is the open neighborhood of $v$ and (ii) every vertex $v$ forwhich $f(v)=-1$ is adjacent to at least one vertex$w$ for which $f(w)\geq 1+\lceil\frac{1}{2}\vert N(w)\cap V_{-1}\vert\rceil$, where$V_{-1}=\{v\in V: f(v)=-1\}$.The minimum of thevalues $\omega(f)=\sum_{v\in V}f(v)$, taken over all signed strongtotal Roman dominating functions $f$ of $G$, is called the signed strong totalRoman domination number of $G$ and is denoted by $\gamma_{ssTR}(G)$.In this paper, we initiate signed strong total Roman domination number of a graph and giveseveral bounds for this parameter. Then, among other results, we determine the signed strong total Roman dominationnumber of special classes of graphs.
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.