Opuscula Math. 38, no. 6 (2018), 779-794

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.

Full text (pdf)

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

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.