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

• Autorzy: Waldemar Szumny , Andrzej Włoch , Iwona Włoch
• Języki publikacji: EN

Abstrakty

EN

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

EN

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

Kategorie tematyczne

• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 3
• Strony: 457-470

Daty

wydano

2007

otrzymano

2006-04-29

poprawiono

2007-05-18

zaakceptowano

2007-05-18

Twórcy

autor

Waldemar Szumny

• Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland

autor

Andrzej Włoch

• Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland

autor

Iwona Włoch

• 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.

Identyfikatory

DOI

10.7151/dmgt.1373