On the existence and number of -kings in -quasi-transitive digraphs
✍ Scribed by Galeana-Sánchez, Hortensia; Hernández-Cruz, César; Juárez-Camacho, Manuel Alejandro
- Book ID
- 123174126
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 437 KB
- Volume
- 313
- Category
- Article
- ISSN
- 0012-365X
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## Abstract A vertex set __X__ of a digraph __D__ = (__V, A__) is a __kernel__ if __X__ is independent (i.e., all pairs of distinct vertices of __X__ are non‐adjacent) and for every __v__ ∈ __V__‐__X__ there exists __x__ ∈ __X__ such that __vx__ ∈ __A__. A vertex set __X__ of a digraph __D__ = (__V
In this paper we present some results on the existence of /c-kernels and (k, [)-kernels in digraphs which generalize the following Theorem of P. Duchet [2]: "If every directed cycle of odd length in a digraph D has at least two symmetrical arcs, then D has a kernel.
This work deals with the domination numbers of generalized de Bruijn digraphs and generalized Kautz digraphs. Dominating sets for digraphs are not familiar compared with dominating sets for undirected graphs. Whereas dominating sets for digraphs have more applications than those for undirected graph