- Tytuł:
- (K − 1)-Kernels In Strong K-Transitive Digraphs
- Autorzy:
- Wang, Ruixia
- Powiązania:
- https://bibliotekanauki.pl/articles/31339493.pdf
- Data publikacji:
- 2015-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
digraph
transitive digraph
k-transitive digraph
k-kernel - Opis:
- Let D = (V (D),A(D)) be a digraph and k ≥ 2 be an integer. A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v) ≥ k; it is l-absorbent if for every u ∈ V (D) − N, there exists v ∈ N such that d(u, v) ≤ l. A (k, l)-kernel of D is a k-independent and l-absorbent subset of V (D). A k-kernel is a (k, k − 1)-kernel. A digraph D is k-transitive if for any path x0x1・・・ xk of length k, x0 dominates xk. Hernández-Cruz [3-transitive digraphs, Discuss. Math. Graph Theory 32 (2012) 205-219] proved that a 3-transitive digraph has a 2-kernel if and only if it has no terminal strong component isomorphic to a 3-cycle. In this paper, we generalize the result to strong k-transitive digraphs and prove that a strong k-transitive digraph with k ≥ 4 has a (k − 1)-kernel if and only if it is not isomorphic to a k-cycle.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2015, 35, 2; 229-235
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł