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

Paweł Bednarz, Iwona Włoch

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.

Keywords


Independence; domination; cartesian product; (2-d)-kernel

Full Text:

PDF

References


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.

Bednarz, P., Włoch, I., An algorithm determining (2-d)-kernels in trees, Util. Math., in print.

Diestel, R., Graph Theory, Springer-Verlag, Heidelberg, New York, 2005.

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.

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.

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

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

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.

Galeana-Sanchez, H., Pastrana-Ramırez, L., Extending digraphs to digraphs with (without) k-kernel, Int. J. Contemp. Math. Sci. 3 (5) (2008), 229-243.

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.

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.

Imrich, W., Klavzar, S., Rall, D. F., Topics in Graph Theory: Graphs and Their Cartesian Product, A. K. Peters Ltd., Wellesley Massachusetts, 2008.

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.

Kwasnik, M., (k, l)-kernels in graphs and in their products, Ph.D. Dissertation, Wrocław, 1980.

Szumny, W., Włoch, A., Włoch, I., On (k, l)-kernels in D-join of digraphs, Discuss. Math. Graph Theory 27 (2007), 457-470.

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.

Włoch, A., On 2-dominating kernels in graphs, Australas. J. Combin. 53 (2012), 273-284.

Włoch, A., Włoch, I., On (k, l)-kernels in generalized products, Discrete Math. 164 (1997), 295-301.

Włoch, A., Włoch, I., On (k, l)-kernels in the corona of digraphs, Int. J. Pure Appl. Math. 53 (4) (2009), 571-582.




DOI: http://dx.doi.org/10.17951/a.2016.70.2.1
Date of publication: 2016-12-24 22:42:00
Date of submission: 2016-12-22 22:43:41


Statistics


Total abstract view - 689
Downloads (from 2020-06-17) - PDF - 364

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 Paweł Bednarz, Iwona Włoch