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Języki publikacji
Abstrakty
The study of nearly perfect sets in graphs was initiated in [2]. Let S ⊆ 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 ∈ V(G) - S, S ∪ {u} is not nearly perfect in G. The minimum cardinality of a maximal nearly perfect set is denoted by np(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 np(G1 x G2) and np(G1 ⊗ G2), for some special graphs G1,G2.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
177--180
Opis fizyczny
Bibliogr. 2 poz.
Twórcy
autor
- Technical University of Szczecin Institute of Mathematics al. Piastów 48/49, 70-310 Szczecin, Poland
autor
Bibliografia
- [1] Diestel R.: Graph Theory. New York, Springer-Verlag 1997.
- [2] Dunbar J.E., Harris F.C., Hedetniemi S.M., Hedetniemi S.T., McRae A. A., Laskar R. C: Nearly perfect sets in graphs. Discrete Mathematics 138 (1995), 229-246.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0005-0075