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| Titel: |
Nearly perfect sets in the n-fold products of graphs |
| Auteur: |
Monika Perl |
| Verschenen in: |
Opuscula mathematica |
| Paginering: | Jaargang 27 (2007) nr. 1 pagina's 83-88 |
| Jaar: |
2007 |
| Inhoud: |
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 $1$-maximal if for every vertex $u \in V(G)-S$, $S \cup \{u\}$ is not nearly perfect in $G$. We denote the minimum cardinality of a $1$-maximal nearly perfect set in $G$ by $n_p(G)$. We will call the $1$-maximal nearly perfect set of the cardinality $n_p(G)$ an $n_p(G)$-set. In this paper, we evaluate the parameter $n_p(G)$ for some $n$-fold products of graphs. To this effect, we determine $1$-maximal nearly perfect sets in the $n$-fold Cartesian product of graphs and in the $n$-fold strong product of graphs. |
| Uitgever: |
AGH University of Science and Technology (provided by DOAJ) |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 6 van 13 gevonden artikelen
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