Geodesic
On the Signed (Total) k-Independence Number in Graphs
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 651-662.

Voir la notice de l'article provenant de la source Library of Science

Let G be a graph. A function f : V (G) → −1, 1 is a signed k- independence function if the sum of its function values over any closed neighborhood is at most k − 1, where k ≥ 2. The signed k-independence number of G is the maximum weight of a signed k-independence function of G. Similarly, the signed total k-independence number of G is the maximum weight of a signed total k-independence function of G. In this paper, we present new bounds on these two parameters which improve some existing bounds.
Keywords: domination in graphs, signed k-independence, limited packing, tuple domination 
@article{DMGT_2015_35_4_a4,
     author = {Khodkar, Abdollah and Samadi, Babak and Volkmann, Lutz},
     title = {On the {Signed} {(Total)} {k-Independence} {Number} in {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {651--662},
     publisher = {mathdoc},
     volume = {35},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a4/}
}
TY  - JOUR
AU  - Khodkar, Abdollah
AU  - Samadi, Babak
AU  - Volkmann, Lutz
TI  - On the Signed (Total) k-Independence Number in Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2015
SP  - 651
EP  - 662
VL  - 35
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a4/
LA  - en
ID  - DMGT_2015_35_4_a4
ER  - 
%0 Journal Article
%A Khodkar, Abdollah
%A Samadi, Babak
%A Volkmann, Lutz
%T On the Signed (Total) k-Independence Number in Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2015
%P 651-662
%V 35
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a4/
%G en
%F DMGT_2015_35_4_a4
Khodkar, Abdollah; Samadi, Babak; Volkmann, Lutz. On the Signed (Total) k-Independence Number in Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 651-662. http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a4/

[1] M. Chellali, O. Favaron, A. Hansberg and L. Volkmann, k-domination and k- independence in graphs: A survey, Graphs Combin. 28 (2012) 1-55. doi:10.1007/s00373-011-1040-3

[2] R. Gallant, G. Gunther, B.L. Hartnell and D.F. Rall, Limited packing in graphs, Discrete Appl. Math. 158 (2010) 1357-1364. doi:10.1016/j.dam.2009.04.014

[3] A.N. Ghameshlou, A. Khodkar and S.M. Sheikholeslami, On the signed bad numbers of graphs, Bulletin of the ICA 67 (2013) 81-93.

[4] F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000) 201-213.

[5] V. Kulli, On n-total domination number in graphs, in: Graph Theory, Combina- torics, Algorithms and Applications, SIAM (Philadelphia, 1991) 319-324.

[6] D.A. Mojdeh, B. Samadi and S.M. Hosseini Moghaddam, Limited packing vs tuple domination in graphs, Ars Combin., to appear.

[7] D.A. Mojdeh, B. Samadi and S.M. Hosseini Moghaddam, Total limited packing in graphs, submitted.

[8] L. Volkmann, Signed k-independence in graphs, Cent. Eur. J. Math. 12 (2014) 517-528. doi:10.2478/s11533-013-0357-y

[9] L. Volkmann, Signed total k-independence number in graphs, Util. Math., to appear.

[10] H.C. Wang and E.F. Shan, Signed total 2-independence in graphs, Util. Math. 74 (2007) 199-206.

[11] H.C. Wang, J. Tong and L. Volkmann, A note on signed total 2-independence in graphs, Util. Math. 85 (2011) 213-223.

[12] D.B. West, Introduction to Graph Theory (Second Edition) (Prentice Hall, USA, 2001).