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.
@article{bwmeta1.element.doi-10_7151_dmgt_1824,
author = {Abdollah Khodkar and Babak Samadi and Lutz Volkmann},
title = {On the Signed (Total) K-Independence Number in Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {651-662},
zbl = {1327.05261},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1824}
}
Abdollah Khodkar; Babak Samadi; Lutz Volkmann. On the Signed (Total) K-Independence Number in Graphs. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 651-662. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1824/
[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[Crossref]
[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[Crossref] | Zbl 1218.05132
[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. | Zbl 1274.05353
[4] F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000) 201-213. | Zbl 0993.05104
[5] V. Kulli, On n-total domination number in graphs, in: Graph Theory, Combina- torics, Algorithms and Applications, SIAM (Philadelphia, 1991) 319-324. | Zbl 0758.05083
[6] D.A. Mojdeh, B. Samadi and S.M. Hosseini Moghaddam, Limited packing vs tuple domination in graphs, Ars Combin., to appear. | Zbl 1267.05194
[7] D.A. Mojdeh, B. Samadi and S.M. Hosseini Moghaddam, Total limited packing in graphs, submitted. | Zbl 1267.05194
[8] L. Volkmann, Signed k-independence in graphs, Cent. Eur. J. Math. 12 (2014) 517-528. doi:10.2478/s11533-013-0357-y[Crossref] | Zbl 1284.05205
[9] L. Volkmann, Signed total k-independence number in graphs, Util. Math., to appear. | Zbl 1327.05261
[10] H.C. Wang and E.F. Shan, Signed total 2-independence in graphs, Util. Math. 74 (2007) 199-206. | Zbl 1183.05062
[11] H.C. Wang, J. Tong and L. Volkmann, A note on signed total 2-independence in graphs, Util. Math. 85 (2011) 213-223. | Zbl 1238.05205
[12] D.B. West, Introduction to Graph Theory (Second Edition) (Prentice Hall, USA, 2001).