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On (k,l)-kernels in D-join of digraphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 457-470 Cet article a éte moissonné depuis la source Library of Science

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In [5] the necessary and sufficient conditions for the existence of (k,l)-kernels in a D-join of digraphs were given if the digraph D is without circuits of length less than k. In this paper we generalize these results for an arbitrary digraph D. Moreover, we give the total number of (k,l)-kernels, k-independent sets and l-dominating sets in a D-join of digraphs.
Keywords: (k,l)-kernel, k-independent set, l-dominating set, D-join, counting 
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Szumny, Waldemar; Włoch, Andrzej; Włoch, Iwona. On (k,l)-kernels in D-join of digraphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 457-470. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a4/

[1] M. Blidia, P. Duchet, H. Jacob and F. Maffray, Some operations preserving the existence of kernels, Discrete Math. 205 (1999) 211-216, doi: 10.1016/S0012-365X(99)00026-6.

[2] R. Diestel, Graph Theory (Springer-Verlag, Heidelberg, New-York, Inc., 2005).

[3] H. Galeana-Sanchez, On the existence of kernels and h-kernels in directed graphs, Discrete Math. 110 (1992) 251-225, doi: 10.1016/0012-365X(92)90713-P.

[4] M. Kucharska, On (k,l)-kernels of orientations of special graphs, Ars Combin. 60 (2001) 137-147.

[5] M. Kucharska, On (k,l)-kernel perfectness of special classes of digraphs, Discuss. Math. Graph Theory 25 (2005) 103-119, doi: 10.7151/dmgt.1265.

[6] M. Kwaśnik and I. Włoch, The total number of generalized stable sets and kernels of graphs, Ars Combin. 55 (2000) 139-146.

[7] A. Włoch and I. Włoch, On (k,l)-kernels in generalized products, Discrete Math. 164 (1997) 295-301, doi: 10.1016/S0012-365X(96)00064-7.

[8] I. Włoch, Generalized Fibonacci polynomial of graphs, Ars Combin. 68 (2003) 49-55.