- Tytuł:
- On non-z(mod k) dominating sets
- Autorzy:
-
Caro, Yair
Jacobson, Michael - Powiązania:
- https://bibliotekanauki.pl/articles/743399.pdf
- Data publikacji:
- 2003
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
dominating set
tree
unicyclic graph - Opis:
- For a graph G, a positive integer k, k ≥ 2, and a non-negative integer with z < k and z ≠ 1, a subset D of the vertex set V(G) is said to be a non-z (mod k) dominating set if D is a dominating set and for all x ∈ V(G), |N[x]∩D| ≢ z (mod k).For the case k = 2 and z = 0, it has been shown that these sets exist for all graphs. The problem for k ≥ 3 is unknown (the existence for even values of k and z = 0 follows from the k = 2 case.) It is the purpose of this paper to show that for k ≥ 3 and with z < k and z ≠ 1, that a non-z(mod k) dominating set exist for all trees. Also, it will be shown that for k ≥ 4, z ≥ 1, 2 or 3 that any unicyclic graph contains a non-z(mod k) dominating set. We also give a few special cases of other families of graphs for which these dominating sets must exist.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2003, 23, 1; 189-199
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł