A note on domination parameters of the conjunction of two special graphs

• Autorzy: Maciej Zwierzchowski
• Języki publikacji: EN

Abstrakty

EN

A dominating set D of G is called a split dominating set of G if the subgraph induced by the subset V(G)-D is disconnected. The cardinality of a minimum split dominating set is called the minimum split domination number of G. Such subset and such number was introduced in [4]. In [2], [3] the authors estimated the domination number of products of graphs. More precisely, they were study products of paths. Inspired by those results we give another estimation of the domination number of the conjunction (the cross product) Pₙ ∧ G. The split domination number of Pₙ ∧ G also is determined. To estimate this number we use the minimum connected domination number $γ_c(G)$.

Słowa kluczowe

EN

domination parameters; conjunction of graphs

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 303-310

Daty

wydano

2001

otrzymano

2001-03-28

poprawiono

2001-09-07

Twórcy

autor

Maciej Zwierzchowski

• Institute of Mathematics, University of Technology of Szczecin, al. Piastów 48/49, 70-310 Szczecin, Poland

Bibliografia

• [1] R. Diestel, Graph Theory (Springer-Verlag, New York, Inc., 1997).
• [2] S. Gravier and A. Khelladi, On the domination number of cross products of graphs, Discrete Math. 145 (1995) 273-277, doi: 10.1016/0012-365X(95)00091-A.
• [3] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs: I, Ars Combin. 18 (1983) 33-44.
• [4] V.R. Kulli and B. Janakiram, The split domination number of a graph, Graph Theory Notes of New York XXXII (1997) 16-19.
• [5] E. Sampathkumar and H.B. Walikar, The connected domination number of graph, J. Math. Phy. Sci. 13 (1979) 607-613.

Identyfikatory

DOI

10.7151/dmgt.1152