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.