Temat: 2-packing, Cartesian product - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On dominating the Cartesian product of a graph and K₂
Autorzy:: Hartnell, Bert
Rall, Douglas
Powiązania:: https://bibliotekanauki.pl/articles/744535.pdf
Data publikacji:: 2004
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: domination
2-packing, Cartesian product
Opis:: 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.
Źródło:: Discussiones Mathematicae Graph Theory; 2004, 24, 3; 389-402
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Improving some bounds for dominating Cartesian products
Autorzy:: Hartnell, Bert
Rall, Douglas
Powiązania:: https://bibliotekanauki.pl/articles/743158.pdf
Data publikacji:: 2003
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: domination number
Cartesian product
Vizing's conjecture
2-packing
Opis:: The study of domination in Cartesian products has received its main motivation from attempts to settle a conjecture made by V.G. Vizing in 1968. He conjectured that γ(G)γ(H) is a lower bound for the domination number of the Cartesian product of any two graphs G and H. Most of the progress on settling this conjecture has been limited to verifying the conjectured lower bound if one of the graphs has a certain structural property. In addition, a number of authors have established bounds for dominating the Cartesian product of any two graphs. We show how it is possible to improve some of these bounds by imposing conditions on both graphs. For example, we establish a new lower bound for the domination number of T T, when T is a tree, and we improve an upper bound of Vizing in the case when one of the graphs has k > 1 dominating sets which cover the vertex set and the other has a dominating set which partitions in a certain way.
Źródło:: Discussiones Mathematicae Graph Theory; 2003, 23, 2; 261-272
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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