On dominating the Cartesian product of a graph and K₂

• Autorzy: Bert L. Hartnell , Douglas F. Rall
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

domination; 2-packing, Cartesian product

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 3
• Strony: 389-402

Daty

wydano

2004

otrzymano

2003-01-20

poprawiono

2004-03-30

Twórcy

autor

Bert L. Hartnell

• Saint Mary's University, Halifax, Nova Scotia, Canada B3H 3C3

autor

Douglas F. Rall

• Furman University, Greenville, SC 29613 USA

Bibliografia

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• [3] B.L. Hartnell and D.F. Rall, On Vizing's conjecture, Congr. Numer. 82 (1991) 87-96.
• [4] B.L. Hartnell and D.F. Rall, Lower bounds for dominating Cartesian products, J. Comb. Math. Comb. Comp. 31 (1999) 219-226.
• [5] B.L. Hartnell and D.F. Rall, Improving some bounds for dominating Cartesian products, Discuss. Math. Graph Theory 23 (2003) 261-272, doi: 10.7151/dmgt.1201.
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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.
• [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.
• [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.
• [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.

Identyfikatory

DOI

10.7151/dmgt.1238