On the signed strong total Roman domination number of graphs

IF 0.7 Q2 MATHEMATICS Tamkang Journal of Mathematics Pub Date : 2022-07-29 DOI:10.5556/j.tkjm.54.2023.3907
A. Mahmoodi, M. Atapour, S. Norouzian
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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.
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关于有符号的强总罗马统治数图
让 $G=(V,E)$ 是一个有限且简单的有序图 $n$ 最大化度 $\Delta$. 图上有符号的强全罗马支配函数 $G$ 是一个函数 $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil\frac{\Delta}{2}\rceil+1\}$ 满足(i)每个顶点的条件 $v$ 的 $G$, $f(N(v))=\sum_{u\in N(v)}f(u)\geq 1$,其中$N(v)$ 开放的社区是什么 $v$ (ii)每个顶点 $v$ 为了什么 $f(v)=-1$ 至少与一个顶点相邻$w$ 为了什么? $f(w)\geq 1+\lceil\frac{1}{2}\vert N(w)\cap V_{-1}\vert\rceil$,其中$V_{-1}=\{v\in V: f(v)=-1\}$值的最小值 $\omega(f)=\sum_{v\in V}f(v)$接管了所有签署的罗马统治职能 $f$ 的 $G$的符号强总罗马统治数 $G$ 表示为 $\gamma_{ssTR}(G)$本文提出了图的签名强总罗马支配数,并给出了该参数的若干界。然后,在其他结果中,我们确定了图的特殊类的符号强总罗马支配数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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.
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