Opuscula Math. 38, no. 6 (2018), 779-794
https://doi.org/10.7494/OpMath.2018.38.6.779
Opuscula Mathematica
On signed arc total domination in digraphs
Leila Asgharsharghi
Abdollah Khodkar
S. M. Sheikholeslami
Abstract. Let \(D=(V,A)\) be a finite simple digraph and \(N(uv)=\{u^{\prime}v^{\prime}\neq uv \mid u=u^{\prime}\text{ or }v=v^{\prime}\}\) be the open neighbourhood of \(uv\) in \(D\). A function \(f: A\rightarrow \{-1, +1\}\) is said to be a signed arc total dominating function (SATDF) of \(D\) if \(\sum _{e^{\prime}\in N(uv)}f(e^{\prime})\geq 1\) holds for every arc \(uv\in A\). The signed arc total domination number \(\gamma^{\prime}_{st}(D)\) is defined as \(\gamma^{\prime}_{st}(D)= \operatorname{min}\{\sum_{e\in A}f(e)\mid f \text{ is an SATDF of }D\}\). In this paper we initiate the study of the signed arc total domination in digraphs and present some lower bounds for this parameter.
Keywords: signed arc total dominating function, signed arc total domination number, domination in digraphs.
Mathematics Subject Classification: 05C69.
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- Leila Asgharsharghi
- Azarbaijan Shahid Madani University, Department of Mathematics, Tabriz, I.R. Iran
- Abdollah Khodkar
- Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA
- S. M. Sheikholeslami
- Azarbaijan Shahid Madani University, Department of Mathematics, Tabriz, I.R. Iran
- Communicated by Andrzej Żak.
- Received: 2016-02-25.
- Revised: 2018-05-21.
- Accepted: 2018-05-22.
- Published online: 2018-07-05.
