Opuscula Math. 36, no. 2 (2016), 145-152
http://dx.doi.org/10.7494/OpMath.2016.36.2.145

 
Opuscula Mathematica

Bounds on the inverse signed total domination numbers in graphs

M. Atapour
S. Norouzian
S. M. Sheikholeslami
L. Volkmann

Abstract. Let \(G=(V,E)\) be a simple graph. A function \(f:V\rightarrow \{-1,1\}\) is called an inverse signed total dominating function if the sum of its function values over any open neighborhood is at most zero. The inverse signed total domination number of \(G\), denoted by \(\gamma_{st}^0(G)\), equals to the maximum weight of an inverse signed total dominating function of \(G\). In this paper, we establish upper bounds on the inverse signed total domination number of graphs in terms of their order, size and maximum and minimum degrees.

Keywords: inverse signed total dominating function, inverse signed total domination number.

Mathematics Subject Classification: 05C69.

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  • M. Atapour
  • Department of Mathematics, University of Bonab, Bonab, I. R. Iran
  • S. Norouzian
  • Azarbaijan Shahid Madani University, Department of Mathematics, Tabriz, I. R. Iran
  • S. M. Sheikholeslami
  • Azarbaijan Shahid Madani University, Department of Mathematics, Tabriz, I. R. Iran
  • L. Volkmann
  • RWTH-Aachen University, Lehrstuhl II für Mathematik, 52056 Aachen, Germany
  • Communicated by Mariusz Meszka.
  • Received: 2014-10-22.
  • Accepted: 2015-07-09.
  • Published online: 2015-12-18.
Opuscula Mathematica - cover

Cite this article as:
M. Atapour, S. Norouzian, S. M. Sheikholeslami, L. Volkmann, Bounds on the inverse signed total domination numbers in graphs, Opuscula Math. 36, no. 2 (2016), 145-152, http://dx.doi.org/10.7494/OpMath.2016.36.2.145

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