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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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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