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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  1. H. Karami, S.M. Sheikholeslami, A. Khodkar, Lower bounds on signed edge total domination numbers in graphs, Czechoslovak Math. J. 3 (2008), 595-603.
  2. W. Meng, On signed edge domination in digraphs, manuscript.
  3. S.M. Sheikholeslami, Signed total domination numbers of directed graphs, Util. Math. 85 (2011), 273-279.
  4. D.B. West, Introduction to Graph Theory, Prentice-Hall, Inc, 2000.
  5. B. Xu, L. Yinquan, On signed edge total domination numbers of graphs, J. Math. Practice Theory 39 (2009), 1-7.
  6. B. Zelinka, On signed edge domination numbers of trees, Math. Bohem. 127 (2002), 49-55.
  7. J. Zhao, B. Xu, On signed edge total domination numbers of graphs, J. Math. Res. Exposition 2 (2011), 209-214.
  • 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.
Opuscula Mathematica - cover

Cite this article as:
Leila Asgharsharghi, Abdollah Khodkar, S. M. Sheikholeslami, On signed arc total domination in digraphs, Opuscula Math. 38, no. 6 (2018), 779-794, https://doi.org/10.7494/OpMath.2018.38.6.779

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