Geodesic
On (2-d)-kernels in the cartesian product of graphs
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 2.

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

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.
Keywords: Independence, domination, cartesian product, (2-d)-kernel 
@article{AUM_2016_70_2_a4,
     author = {Bednarz, Pawe{\l} and W{\l}och, Iwona},
     title = {On (2-d)-kernels in the cartesian product of graphs},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {70},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a4/}
}
TY  - JOUR
AU  - Bednarz, Paweł
AU  - Włoch, Iwona
TI  - On (2-d)-kernels in the cartesian product of graphs
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2016
VL  - 70
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a4/
LA  - en
ID  - AUM_2016_70_2_a4
ER  - 
%0 Journal Article
%A Bednarz, Paweł
%A Włoch, Iwona
%T On (2-d)-kernels in the cartesian product of graphs
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2016
%V 70
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a4/
%G en
%F AUM_2016_70_2_a4
Bednarz, Paweł; Włoch, Iwona. On (2-d)-kernels in the cartesian product of graphs. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 2. http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a4/

[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.

[5] Galeana-Sanchez, H., Hernandez-Cruz, C., On the existence of k-kernels in digraphs and in weighted digraphs, AKCE Int. J. Graphs Comb. 7 (2) (2010), 201-215.

[6] Galeana-Sanchez, H., Hernandez-Cruz, C., k-kernels in generalizations of transitive digraphs, Discuss. Math. Graph Theory 31 (2) (2011), 293-312.

[7] Galeana-Sanchez, H., Hernandez-Cruz, C., Cyclically k-partite digraphs and k-kernels, Discuss. Math. Graph Theory 31 (1) (2011), 63-78.

[8] Galeana-Sanchez, H., Hernandez-Cruz, C., On the existence of (k, l)-kernels in infinite digraphs: A survey, Discuss. Math. Graph Theory 34 (3) (2014), 431-466.

[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.

[10] Galeana-Sanchez, H., Pastrana-Ramırez, L., k-kernels in the orientation of the path graph, Int. J. Contemp. Math. Sci. 5 (5) (2010), 231-242.

[11] Galeana-Sanchez, H., Pastrana-Ramırez, L., A construction that preserves the number of k-kernels, Int. J. Contemp. Math. Sci. 6 (10) (2011), 491-502.

[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.