Geodesic
On (k,l)-kernels in D-join of digraphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 457-470

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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/