- Tytuł:
- About (k, l)-Kernels, Semikernels and Grundy Functions in Partial Line Digraphs
- Autorzy:
-
Balbuena, C.
Galeana-Sánchez, H.
Guevara, M. - Tematy:
-
digraphs
in-domination
kernel
Grundy function - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/31343207.pdf Link otwiera się w nowym oknie
- Opis:
- Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 ≤ l ≤ k, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial line digraph ℒD. Moreover, if l < k and the girth of D is at least l +1, then these two numbers are equal. We also prove that the number of semikernels of D is equal to the number of semikernels of ℒD. Furthermore, we introduce the concept of (k, l)-Grundy function as a generalization of the concept of Grundy function and we prove that the number of (k, l)-Grundy functions of D is equal to the number of (k, l)-Grundy functions of any partial line digraph ℒD.
- Dostawca treści:
- Biblioteka Nauki
Artykuł