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.