On the inverse signed total domination number in graphs

Abstract

In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on $K_{r+1}$-free graphs for $r\geq 2$. Also, we bound this parameter for a tree from below in terms of its order and the number of leaves and characterize all trees attaining this bound.