# On dominating the Cartesian product of a graph and K₂

Bert L. Hartnell; Douglas F. Rall

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 3, page 389-402
- ISSN: 2083-5892

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topBert L. Hartnell, and Douglas F. Rall. "On dominating the Cartesian product of a graph and K₂." Discussiones Mathematicae Graph Theory 24.3 (2004): 389-402. <http://eudml.org/doc/270156>.

@article{BertL2004,

abstract = {In this paper we consider the Cartesian product of an arbitrary graph and a complete graph of order two. Although an upper and lower bound for the domination number of this product follow easily from known results, we are interested in the graphs that actually attain these bounds. In each case, we provide an infinite class of graphs to show that the bound is sharp. The graphs that achieve the lower bound are of particular interest given the special nature of their dominating sets and are investigated further.},

author = {Bert L. Hartnell, Douglas F. Rall},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination; 2-packing, Cartesian product; domination number},

language = {eng},

number = {3},

pages = {389-402},

title = {On dominating the Cartesian product of a graph and K₂},

url = {http://eudml.org/doc/270156},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Bert L. Hartnell

AU - Douglas F. Rall

TI - On dominating the Cartesian product of a graph and K₂

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 3

SP - 389

EP - 402

AB - In this paper we consider the Cartesian product of an arbitrary graph and a complete graph of order two. Although an upper and lower bound for the domination number of this product follow easily from known results, we are interested in the graphs that actually attain these bounds. In each case, we provide an infinite class of graphs to show that the bound is sharp. The graphs that achieve the lower bound are of particular interest given the special nature of their dominating sets and are investigated further.

LA - eng

KW - domination; 2-packing, Cartesian product; domination number

UR - http://eudml.org/doc/270156

ER -

## References

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- [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 209, Marcel Dekker, Inc., New York, 1998. Zbl0883.00011
- [8] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition, Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, Inc., New York, 2000.
- [9] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs: I, Ars Combin. 18 (1983) 33-44. Zbl0566.05050
- [10] M.S. Jacobson and L.F. Kinch, On the domination of the products of graphs II: trees, J. Graph Theory 10 (1986) 97-106, doi: 10.1002/jgt.3190100112. Zbl0584.05053
- [11] V.G. Vizing, The Cartesian product of graphs, Vycisl. Sistemy 9 (1963) 30-43.
- [12] V.G. Vizing, Some unsolved problems in graph theory, Uspehi Mat. Nauk 23 no. 6(144) (1968) 117-134. Zbl0177.52301

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