On (2-d)-kernels in the cartesian product of graphs

Paweł Bednarz; Iwona Włoch

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2016)

  • Volume: 70, Issue: 2
  • ISSN: 0365-1029

Abstract

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In this paper we study the problem of the existence of (2-d)-kernels in the cartesian product of graphs. We give sufficient conditions for the existence of (2-d)-kernels in the cartesian product and also we consider the number of (2-d)-kernels.

How to cite

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Paweł Bednarz, and Iwona Włoch. "On (2-d)-kernels in the cartesian product of graphs." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 70.2 (2016): null. <http://eudml.org/doc/289729>.

@article{PawełBednarz2016,
abstract = {In this paper we study the problem of the existence of (2-d)-kernels in the cartesian product of graphs. We give sufficient conditions for the existence of (2-d)-kernels in the cartesian product and also we consider the number of (2-d)-kernels.},
author = {Paweł Bednarz, Iwona Włoch},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Independence; domination; cartesian product; (2-d)-kernel},
language = {eng},
number = {2},
pages = {null},
title = {On (2-d)-kernels in the cartesian product of graphs},
url = {http://eudml.org/doc/289729},
volume = {70},
year = {2016},
}

TY - JOUR
AU - Paweł Bednarz
AU - Iwona Włoch
TI - On (2-d)-kernels in the cartesian product of graphs
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2016
VL - 70
IS - 2
SP - null
AB - In this paper we study the problem of the existence of (2-d)-kernels in the cartesian product of graphs. We give sufficient conditions for the existence of (2-d)-kernels in the cartesian product and also we consider the number of (2-d)-kernels.
LA - eng
KW - Independence; domination; cartesian product; (2-d)-kernel
UR - http://eudml.org/doc/289729
ER -

References

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  1. Bednarz, P., Hernandez-Cruz, C., Włoch, I., On the existence and the number of (2-d)-kernels in graphs, Ars Combin. 121 (2015), 341-351. 
  2. Bednarz, P., Włoch, I., An algorithm determining (2-d)-kernels in trees, Util. Math., in print. 
  3. Diestel, R., Graph Theory, Springer-Verlag, Heidelberg, New York, 2005. 
  4. Galeana-Sanchez, H., Gomez, R., (k, l)-kernels, (k, l)-semikernels, k-Grundy functions and duality for state splittings, Discuss. Math. Graph Theory 27 (2007), 359-371. 
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  9. Galeana-Sanchez, H., Pastrana-Ramırez, L., Extending digraphs to digraphs with (without) k-kernel, Int. J. Contemp. Math. Sci. 3 (5) (2008), 229-243. 
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  12. Imrich, W., Klavzar, S., Rall, D. F., Topics in Graph Theory: Graphs and Their Cartesian Product, A. K. Peters Ltd., Wellesley Massachusetts, 2008. 
  13. Kucharska, M., Kwasnik, M., On (k, l)-kernels of special superdigraphs of P m and C m , Discuss. Math. Graph Theory 21 (1) (2001), 95-109. 
  14. Kwasnik, M., (k, l)-kernels in graphs and in their products, Ph.D. Dissertation, Wrocław, 1980. 
  15. Szumny, W., Włoch, A., Włoch, I., On (k, l)-kernels in D-join of digraphs, Discuss. Math. Graph Theory 27 (2007), 457-470. 
  16. Szumny, W., Włoch, A., Włoch, I., On the existence and on the number of (k, l)-kernels in the lexicographic product of graphs, Discrete Math. 308 (20) (2008), 4616-4624. 
  17. Włoch, A., On 2-dominating kernels in graphs, Australas. J. Combin. 53 (2012), 273-284. 
  18. Włoch, A., Włoch, I., On (k, l)-kernels in generalized products, Discrete Math. 164 (1997), 295-301. 
  19. Włoch, A., Włoch, I., On (k, l)-kernels in the corona of digraphs, Int. J. Pure Appl. Math. 53 (4) (2009), 571-582. 

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