Geodesic
Upper signed total domination number of directed graphs
Kragujevac Journal of Mathematics, Tome 36 (2012) no. 2, p. 349 .

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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 $ȁmma^s_{t}(D)$.
Classification : 05C69 05C20
Keywords: Signed total dominating function, minimal signed total dominating function, upper signed total domination number, directed graph. 
@article{KJM_2012_36_2_a17,
     author = {Seyed Mahmoud Sheikholeslami},
     title = {Upper signed total domination number of directed graphs},
     journal = {Kragujevac Journal of Mathematics},
     pages = {349 },
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2012_36_2_a17/}
}
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Seyed Mahmoud Sheikholeslami. Upper signed total domination number of directed graphs. Kragujevac Journal of Mathematics, Tome 36 (2012) no. 2, p. 349 . http://geodesic.mathdoc.fr/item/KJM_2012_36_2_a17/