On the Signed (Total) K-Independence Number in Graphs

Abdollah Khodkar; Babak Samadi; Lutz Volkmann

Discussiones Mathematicae Graph Theory (2015)

  • Volume: 35, Issue: 4, page 651-662
  • ISSN: 2083-5892

Abstract

top
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.

How to cite

top

Abdollah Khodkar, Babak Samadi, and Lutz Volkmann. "On the Signed (Total) K-Independence Number in Graphs." Discussiones Mathematicae Graph Theory 35.4 (2015): 651-662. <http://eudml.org/doc/275873>.

@article{AbdollahKhodkar2015,
abstract = {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.},
author = {Abdollah Khodkar, Babak Samadi, Lutz Volkmann},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination in graphs; signed k-independence; limited packing; tuple domination; signed -independence},
language = {eng},
number = {4},
pages = {651-662},
title = {On the Signed (Total) K-Independence Number in Graphs},
url = {http://eudml.org/doc/275873},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Abdollah Khodkar
AU - Babak Samadi
AU - Lutz Volkmann
TI - On the Signed (Total) K-Independence Number in Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 4
SP - 651
EP - 662
AB - 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.
LA - eng
KW - domination in graphs; signed k-independence; limited packing; tuple domination; signed -independence
UR - http://eudml.org/doc/275873
ER -

References

top
  1. [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. [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] Zbl1218.05132
  3. [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. Zbl1274.05353
  4. [4] F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000) 201-213. Zbl0993.05104
  5. [5] V. Kulli, On n-total domination number in graphs, in: Graph Theory, Combina- torics, Algorithms and Applications, SIAM (Philadelphia, 1991) 319-324. Zbl0758.05083
  6. [6] D.A. Mojdeh, B. Samadi and S.M. Hosseini Moghaddam, Limited packing vs tuple domination in graphs, Ars Combin., to appear. Zbl1267.05194
  7. [7] D.A. Mojdeh, B. Samadi and S.M. Hosseini Moghaddam, Total limited packing in graphs, submitted. Zbl1267.05194
  8. [8] L. Volkmann, Signed k-independence in graphs, Cent. Eur. J. Math. 12 (2014) 517-528. doi:10.2478/s11533-013-0357-y[Crossref] Zbl1284.05205
  9. [9] L. Volkmann, Signed total k-independence number in graphs, Util. Math., to appear. Zbl1327.05261
  10. [10] H.C. Wang and E.F. Shan, Signed total 2-independence in graphs, Util. Math. 74 (2007) 199-206. Zbl1183.05062
  11. [11] H.C. Wang, J. Tong and L. Volkmann, A note on signed total 2-independence in graphs, Util. Math. 85 (2011) 213-223. Zbl1238.05205
  12. [12] D.B. West, Introduction to Graph Theory (Second Edition) (Prentice Hall, USA, 2001). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.