Temat: domination set - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Independent set dominanting sets in bipartite graphs
Autorzy:: Zelinka, B.
Powiązania:: https://bibliotekanauki.pl/articles/255203.pdf
Data publikacji:: 2005
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: set dominanting set
set domination number
independent set
bipartite graph
multihypergraph
Opis:: The paper continues the study of independent set dominating sets in graphs which was started by E. Sampathkumar. A subset D of the vertex set V(G) of a graph G is called a set dominating set (shortly sd-set) in G, if for each set X ikkeq V(G) - D there exists a set Y ikkeq D such that the subgraph of G induced X cup Y is connected. The minimum number of vertices of an sd-set in G is called the set domination number gammas (G) of G. An sd-set D in G such that /D/ = gammas(G) is called a gammas-set in G. In this paper we study sd-sets in bipartite graphs which are simultaneously independent. We apply the theory of hypergraphs.
Źródło:: Opuscula Mathematica; 2005, 25, 2; 345-349
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Counterexample to a conjecture on the structure of bipartite partitionable graphs
Autorzy:: Gibson, Richard
Mynhardt, Christina
Powiązania:: https://bibliotekanauki.pl/articles/743437.pdf
Data publikacji:: 2007
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: domination
prism fixer
symmetric dominating set
bipartite graph
Opis:: A graph G is called a prism fixer if γ(G×K₂) = γ(G), where γ(G) denotes the domination number of G. A symmetric γ-set of G is a minimum dominating set D which admits a partition D = D₁∪ D₂ such that $V(G)-N[D_i] = D_j$, i,j = 1,2, i ≠ j. It is known that G is a prism fixer if and only if G has a symmetric γ-set.
Hartnell and Rall [On dominating the Cartesian product of a graph and K₂, Discuss. Math. Graph Theory 24 (2004), 389-402] conjectured that if G is a connected, bipartite graph such that V(G) can be partitioned into symmetric γ-sets, then G ≅ C₄ or G can be obtained from $K_{2t,2t}$ by removing the edges of t vertex-disjoint 4-cycles. We construct a counterexample to this conjecture and prove an alternative result on the structure of such bipartite graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2007, 27, 3; 527-540
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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