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Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
457-470
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-04-29
poprawiono
2007-05-18
zaakceptowano
2007-05-18
Twórcy
autor
- Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland
autor
- Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland
autor
- Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland
Bibliografia
- [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1373