Some notes on isolated signed total domination number for digraphs

Abstract

An isolated signed total dominating function (ISTDF) of a digraph is a function \(f: V(D) \rightarrow\{-1,+1\}\) such that \(\sum_u \in N-(v) \geq 1\) for every vertex \(v \in V(D)\) and for at least one vertex of \(w \in V(D), f\left(N^{-}(w)\right)=+1\). An isolated signed totaldomination number of \(\mathrm{D}\), denoted by \(\gamma_{\text {ist }}(D)\), in the minimal weight of an isolated signed total dominating function of \(D\). In this paper, we study some properties of ISTDF.