Twin signed domination numbers in directed graphs
Algebra and discrete mathematics, Tome 24 (2017) no. 1, pp. 71-89.

Voir la notice de l'article dans Math-Net.Ru

Let $D=(V,A)$ be a finite simple directed graph (shortly digraph). A function $f\colon V\to \{-1,1\}$ is called a twin signed dominating function (TSDF) if $f(N^-[v])\ge 1$ and $f(N^+[v])\ge 1$ for each vertex $v\in V$. The twin signed domination number of $D$ is $\gamma_{s}^*(D)=\min\{\omega(f)\mid f \text{ is a TSDF of } D\}$. In this paper, we initiate the study of twin signed domination in digraphs and we present sharp lower bounds for $\gamma_{s}^*(D)$ in terms of the order, size and maximum and minimum indegrees and outdegrees. Some of our results are extensions of well-known lower bounds of the classical signed domination numbers of graphs.
Mots-clés : twin signed dominating function, twin signed domination number, directed graph. 
@article{ADM_2017_24_1_a4,
     author = {M. Atapour and S. Norouzian and S. M. Sheikholeslami and L. Volkmann},
     title = {Twin signed domination numbers in directed graphs},
     journal = {Algebra and discrete mathematics},
     pages = {71--89},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2017},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/ADM_2017_24_1_a4/}
}
TY  - JOUR
AU  - M. Atapour
AU  - S. Norouzian
AU  - S. M. Sheikholeslami
AU  - L. Volkmann
TI  - Twin signed domination numbers in directed graphs
JO  - Algebra and discrete mathematics
PY  - 2017
SP  - 71
EP  - 89
VL  - 24
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/ADM_2017_24_1_a4/
LA  - en
ID  - ADM_2017_24_1_a4
ER  - 
%0 Journal Article
%A M. Atapour
%A S. Norouzian
%A S. M. Sheikholeslami
%A L. Volkmann
%T Twin signed domination numbers in directed graphs
%J Algebra and discrete mathematics
%D 2017
%P 71-89
%V 24
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/ADM_2017_24_1_a4/
%G en
%F ADM_2017_24_1_a4
M. Atapour; S. Norouzian; S. M. Sheikholeslami; L. Volkmann. Twin signed domination numbers in directed graphs. Algebra and discrete mathematics, Tome 24 (2017) no. 1, pp. 71-89. https://geodesic-test.mathdoc.fr/item/ADM_2017_24_1_a4/

[1] S. Arumugam, K. Ebadi and L. Sathikala, “Twin domination and twin irredundance in digraphs”, Appl. Anal. Discrete Math., 7 (2013), 275–284 | DOI | MR | Zbl

[2] M. Atapour, R. Hajypory, S. M. Sheikholeslami and L. Volkmann, “The signed k-domination number of directed graphs”, Cent. Eur. J. Math., 8 (2010), 1048–1057 | DOI | MR | Zbl

[3] G. Chartrand, P. Dankelmann, M. Schultz and H. C. Swart, “Twin domination in digraphs”, Ars Combin., 67 (2003), 105–114 | MR | Zbl

[4] J. E. Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater, “Signed domination in graphs”, Graph Theory, Combinatorics, and Applications, Proc. 7th Internat. Conf. Combinatorics, Graph Theory, Applications, v. 1, eds. Y. Alavi and A. J. Schwenk, John Wiley and Sons, Inc., 1995, 311–322 | MR

[5] M. A. Henning and P. J. Slater, “Inequalities relating domination parameters in cubic graphs”, Discrete Math., 158 (1996), 87–98 | DOI | MR | Zbl

[6] H. Karami, A. Khodkar and S. M. Sheikholeslami, “Lower bounds on signed domination number of a digraph”, Discrete Math., 309 (2009), 2567–2570 | DOI | MR | Zbl

[7] C. Wang, “The signed $k$-domination numbers in graphs”, Ars Combin., 106 (2012), 205–211 | MR | Zbl

[8] D. B. West, Introduction to Graph Theory, Prentice-Hall, Inc, 2000 | MR

[9] B. Zelinka, “Signed domination numbers of directed graphs”, Czechoslovak Math. J., 55 (2005), 479–482 | DOI | MR | Zbl

[10] Z. Zhang, B. Xu, Y. Li and L. Liu, “A note on the lower bounds of signed domination number of a graph”, Discrete Math., 195 (1999), 295–298 | DOI | MR | Zbl