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.

Full text (pdf)

1. M.A. Henning, Signed total domination in graphs, Discrete Math. 278 (2004), 109-125.
2. Z. Huang, Z. Feng, H. Xing, Inverse signed total domination numbers of some kinds of graphs, Information Computing and Applications Communications in Computer and Information Science ICICA 2012, Part II, CCIS 308, 315-321, 2012.
3. D.B. West, Introduction to Graph Theory, Prentice-Hall, Inc., 2000.
4. B. Zelinka, Signed total domination number of a graph, Czechoslovak Math. J. 51 (2001), 225-229.
• 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.
• Accepted: 2015-07-09.
• Published online: 2015-12-18.