# On (k,l)-kernels in D-join of digraphs

Waldemar Szumny; Andrzej Włoch; Iwona Włoch

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 3, page 457-470
- ISSN: 2083-5892

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topWaldemar Szumny, Andrzej Włoch, and Iwona Włoch. "On (k,l)-kernels in D-join of digraphs." Discussiones Mathematicae Graph Theory 27.3 (2007): 457-470. <http://eudml.org/doc/270343>.

@article{WaldemarSzumny2007,

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.},

author = {Waldemar Szumny, Andrzej Włoch, Iwona Włoch},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {(k,l)-kernel; k-independent set; l-dominating set; D-join; counting; -kernel; -independent set, -dominating set; -join},

language = {eng},

number = {3},

pages = {457-470},

title = {On (k,l)-kernels in D-join of digraphs},

url = {http://eudml.org/doc/270343},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Waldemar Szumny

AU - Andrzej Włoch

AU - Iwona Włoch

TI - On (k,l)-kernels in D-join of digraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 3

SP - 457

EP - 470

AB - 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.

LA - eng

KW - (k,l)-kernel; k-independent set; l-dominating set; D-join; counting; -kernel; -independent set, -dominating set; -join

UR - http://eudml.org/doc/270343

ER -

## References

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- [2] R. Diestel, Graph Theory (Springer-Verlag, Heidelberg, New-York, Inc., 2005).
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- [4] M. Kucharska, On (k,l)-kernels of orientations of special graphs, Ars Combin. 60 (2001) 137-147. Zbl1068.05504
- [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. Zbl1074.05043
- [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. Zbl1071.05556

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