Weak Signed Roman Domination in Digraphs

Authors

DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3523

Keywords:

Digraph, Signed Roman domination number, Weak signed Roman domination number

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 all vertices 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 classes of digraphs.

References

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Published

2021-10-30

How to Cite

Volkmann, L. (2021). Weak Signed Roman Domination in Digraphs. Tamkang Journal of Mathematics, 52(4), 497-508. https://doi.org/10.5556/j.tkjm.52.2021.3523

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Papers

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