Twin signed Roman domination numbers in directed graphs

Authors

  • Seyed Mahmoud Sheikholeslami
  • Asghar Bodaghli
  • Lutz Volkmann

DOI:

https://doi.org/10.5556/j.tkjm.47.2016.2035

Keywords:

twin signed Roman dominating function, twin signed Roman domination number, directed graph

Abstract

Let $D$ be a finite simple digraph with vertex set $V(D)$ and arc set $A(D)$. A twin signed Roman dominating function (TSRDF) on the digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2\}$ satisfying the conditions that (i) $\sum_{x\in N^-[v]}f(x)\ge 1$ and $\sum_{x\in N^+[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ (resp. $N^+[v]$) consists of $v$ and all in-neighbors (resp. out-neighbors) of $v$, and (ii) every vertex $u$ for which $f(u)=-1$ has an in-neighbor $v$ and an out-neighbor $w$ for which $f(v)=f(w)=2$. The weight of an TSRDF $f$ is $\omega(f)=\sum_{v\in V(D)}f(v)$. The twin signed Roman domination number $\gamma_{sR}^*(D)$ of $D$ is the minimum weight of an TSRDF on $D$. In this paper, we initiate the study of twin signed Roman domination in digraphs and we present some sharp bounds on $\gamma_{sR}^*(D)$. In addition, we determine the twin signed Roman domination number of some classes of digraphs.

Author Biographies

Seyed Mahmoud Sheikholeslami

Department ofMathematics, Azarbaijan ShahidMadani University, Tabriz, I.R. Iran.

Asghar Bodaghli

Department ofMathematics, Azarbaijan ShahidMadani University, Tabriz, I.R. Iran.

Lutz Volkmann

Lehrstuhl II f├╝rMathematik, RWTH Aachen University, 52056 Aachen, Germany.

References

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Published

2016-09-30

How to Cite

Sheikholeslami, S. M., Bodaghli, A., & Volkmann, L. (2016). Twin signed Roman domination numbers in directed graphs. Tamkang Journal of Mathematics, 47(3), 357-371. https://doi.org/10.5556/j.tkjm.47.2016.2035

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