Weak Signed Roman Domination in Digraphs

IF 0.7 Q2 MATHEMATICS
L. Volkmann
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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.
有向图中的弱签名罗马统治
设$D$是一个顶点集$V(D)$的有限简单有向图。有向图$D$上的弱符号罗马支配函数(WSRDF)是一个满足如下条件的函数$f:V(D)\rightarrow\{-1,1,2\}$: $\sum_{x\in N^-[v]}f(x)\ge 1$对于每个$v\in V(D)$,其中$N^-[v]$由$v$和$D$的所有顶点组成,弧从这些顶点进入$v$。WSRDF $f$的权重为$\sum_{v\in V(D)}f(v)$。$D$的弱签名罗马支配数$\gamma_{wsR}(D)$是$D$上WSRDF的最小权重。本文研究了有向图的弱签名罗马支配数,并在$\gamma_{wsR}(D)$上给出了不同的界。此外,我们还确定了一些有向图类的弱签名罗马支配数。
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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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