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

• Volume: 21, Issue: 2, page 303-310
• ISSN: 2083-5892

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## Abstract

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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 ${\gamma }_{c}\left(G\right)$.

## How to cite

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Maciej Zwierzchowski. "A note on domination parameters of the conjunction of two special graphs." Discussiones Mathematicae Graph Theory 21.2 (2001): 303-310. <http://eudml.org/doc/270396>.

@article{MaciejZwierzchowski2001,
abstract = {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 $γ_c(G)$.},
author = {Maciej Zwierzchowski},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domination parameters; conjunction of graphs; dominating set; split dominating; split domination number; connected domination number},
language = {eng},
number = {2},
pages = {303-310},
title = {A note on domination parameters of the conjunction of two special graphs},
url = {http://eudml.org/doc/270396},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Maciej Zwierzchowski
TI - A note on domination parameters of the conjunction of two special graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2001
VL - 21
IS - 2
SP - 303
EP - 310
AB - 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 $γ_c(G)$.
LA - eng
KW - domination parameters; conjunction of graphs; dominating set; split dominating; split domination number; connected domination number
UR - http://eudml.org/doc/270396
ER -

## References

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1. [1] R. Diestel, Graph Theory (Springer-Verlag, New York, Inc., 1997).
2. [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. Zbl0833.05053
3. [3] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs: I, Ars Combin. 18 (1983) 33-44. Zbl0566.05050
4. [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. [5] E. Sampathkumar and H.B. Walikar, The connected domination number of graph, J. Math. Phy. Sci. 13 (1979) 607-613. Zbl0449.05057

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