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.
• Revised: 2018-05-21.
• Accepted: 2018-05-22.
• Published online: 2018-07-05.