An introduction to the twin signed total k-domination numbers in directed graphs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1331-1343.

Let D=(V,A) be a finite simple directed graph (shortly digraph), N - (v) and N + (v) denote the set of in-neighbors and out-neighbors of a vertex vV, respectively. A function f:V-{-1,1} is called a twin signed total k-dominating function (TSTkDF) if u(N - (v))f(u)k and u(N + (v))f(u)k for each vertex vV. The twin signed total k-domination number of D is γ stk * (D)=min{ω(f)|f is a TSTkDF of D}, where ω(f)= vV f(v) is the weight of f. In this paper, we initiate the study of twin signed total k-domination in digraphs and present different bounds on γ stk * (D). In addition, we determine the twin signed total k-domination number of some classes of digraphs. Our results are mostly extensions of well-known bounds of the twin signed total domination numbers of directed graphs.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017036
Classification : 05C69
Mots-clés : Twin signed total k-dominating function, twin signed total k-domination number, directed graph
Atapour, Maryam 1 ; Dehgardi, Nasrin 2 ; Volkmann, L. 3

1 Department of Mathematics, Faculty of basic sciences, University of Bonab, Bonab, I.R. Iran.
2 Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, I.R. Iran.
3 Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany.
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     title = {An introduction to the twin signed total $k$-domination numbers in directed graphs},
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Atapour, Maryam; Dehgardi, Nasrin; Volkmann, L. An introduction to the twin signed total $k$-domination numbers in directed graphs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1331-1343. doi : 10.1051/ro/2017036. http://www.numdam.org/articles/10.1051/ro/2017036/

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