Upper signed total domination number of directed graphs


Seyed Mahmoud Sheikholeslami




Let $D=(V,A)$ be a finite simple digraph in which $d^-_D(v)\ge 1$ for all $vı V$. A function $f:Vongrightarrow \{-1,1\}$ is called a signed total dominating function (STDF) if $um_{uı N^-(v)}f(u) \ge 1$ for each vertex $vı V$. A STDF $f$ of a digraph $D$ is minimal if there is no STDF $geq f$ such that $g(v)e f(v)$ for each $vı V$. The maximum value of $um_{vı V}f(v)$, taken over all minimal signed total dominating functions $f$, is called the {\em upper signed total domination number} $ȁmma_{t}^s(D)$. In this paper, we present a sharp upper bound for $ȁmma^s_{t}(D)$.