Opuscula Math. 36, no. 2 (), 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

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.