- Tytuł:
- Nearly perfect sets in products of graphs
- Autorzy:
-
Kwaśnik, M.
Perl, M. - Powiązania:
- https://bibliotekanauki.pl/articles/2050769.pdf
- Data publikacji:
- 2004
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
dominating sets
product of graphs - Opis:
- The study of nearly perfect sets in graphs was initiated in [2]. Let $S \subseteq V(G)$. We say that $S$ is a nearly perfect set (or is nearly perfect) in $G$ if every vertex in $V(G) - S$ is adjacent to at most one vertex in $S$. A nearly perfect set $S$ in $G$ is called maximal if for every vertex $u \in V(G) - S, S \cup \{u\}$ is not nearly perfect in $G$. The minimum cardinality of a maximal nearly perfect set is denoted by $n_{p}(G)$. It is our purpose in this paper to determine maximal nearly perfect sets in two well-known products of two graphs, i.e. in the Cartesian product and in the strong product. Lastly, we give upper bounds of $n_{p}(G1 \times G2)$ and $n_{p}(G1 \otimes G2)$, for some special graphs $G1,G2$.
- Źródło:
-
Opuscula Mathematica; 2004, 24, 2; 177-180
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł