Discussiones Mathematicae Graph Theory 27(3) (2007) 457-470
doi: 10.7151/dmgt.1373

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ON (k,l)-KERNELS IN D-JOIN OF DIGRAPHS

Waldemar Szumny, Andrzej Włoch  and  Iwona Włoch

Faculty of Mathematics and Applied Physics
Rzeszów University of Technology
W. Pola 2, 35-959 Rzeszów, Poland
e-mail: awloch@prz.edu.pl
e-mail: iwloch@prz.edu.pl

Abstract

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.

2000 Mathematics Subject Classification: 05C20.

References

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Received 29 April 2006
Revised 18 May 2007
Accepted 18 May 2007