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

• Autorzy: Abdollah Khodkar , Babak Samadi , Lutz Volkmann
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

domination in graphs; signed k-independence; limited packing; tuple domination

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 4
• Strony: 651-662

Daty

wydano

2015-11-01

otrzymano

2014-09-23

poprawiono

2015-02-11

zaakceptowano

2015-02-11

online

2015-11-10

Twórcy

autor

Abdollah Khodkar

• Department of Mathematics University of West Georgia Carrollton, GA 30118, USA

autor

Babak Samadi

• Department of Mathematics Arak University Arak, Iran

autor

Lutz Volkmann

• Lehrstuhl II für Mathematik RWTH Aachen University 52056 Aachen, Germany

Bibliografia

• [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]
• [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[Crossref]
• [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).

Identyfikatory

DOI

10.7151/dmgt.1824