Autor: Topp, Jerzy - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets
Autorzy:: Henning, Michael A.
Topp, Jerzy
Powiązania:: https://bibliotekanauki.pl/articles/32222686.pdf
Data publikacji:: 2021-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: domination
paired-domination
Opis:: A subset D ⊆ V_G is a dominating set of G if every vertex in V_G – D has a neighbor in D, while D is a paired-dominating set of G if D is a dominating set and the subgraph induced by D contains a perfect matching. A graph G is a DPDP -graph if it has a pair (D, P) of disjoint sets of vertices of G such that D is a dominating set and P is a paired-dominating set of G. The study of the DPDP -graphs was initiated by Southey and Henning [Cent. Eur. J. Math. 8 (2010) 459–467; J. Comb. Optim. 22 (2011) 217–234]. In this paper, we provide conditions which ensure that a graph is a DPDP -graph. In particular, we characterize the minimal DPDP -graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2021, 41, 3; 827-847
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Domination Subdivision and Domination Multisubdivision Numbers of Graphs
Autorzy:: Dettlaff, Magda
Raczek, Joanna
Topp, Jerzy
Powiązania:: https://bibliotekanauki.pl/articles/31343212.pdf
Data publikacji:: 2019-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: domination
domination subdivision number
domination multisubdivision number
trees
computational complexity
Opis:: The domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T) ≤ 3 for any tree T. We prove that the decision problem of the domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the domination multisubdivision number of a nonempty graph G as a minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. We show that msd(G) ≤ 3 for any graph G. The domination subdivision number and the domination multisubdivision number of a graph are incomparable in general, but we show that for trees these two parameters are equal. We also determine the domination multisubdivision number for some classes of graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 4; 829-839
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: On Accurate Domination in Graphs
Autorzy:: Cyman, Joanna
Henning, Michael A.
Topp, Jerzy
Powiązania:: https://bibliotekanauki.pl/articles/31343372.pdf
Data publikacji:: 2019-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: domination number
accurate domination number
tree
corona
Opis:: A dominating set of a graph G is a subset D ⊆ V_G such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of G, denoted by γ_a(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of V_G \ D is a dominating set of G. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees G for which γ_a(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 3; 615-627
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Graphs with equal domination and certified domination numbers
Autorzy:: Dettlaff, Magda
Lemańska, Magdalena
Miotk, Mateusz
Topp, Jerzy
Ziemann, Radosław
Żyliński, Paweł
Powiązania:: https://bibliotekanauki.pl/articles/255932.pdf
Data publikacji:: 2019
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: domination
certified domination
Opis:: A set D of vertices of a graph G = (VG, EG) is a dominating set of G if every vertex in VG — D is adjacent to at least one vertex in D. The domination number (upper domination number, respectively) of G, denoted by [formula], respectively), is the cardinality of a smallest (largest minimal, respectively) dominating set of G. A subset D ⊆ VG is called a certified dominating set of G if D is a dominating set of G and every vertex in D has either zero or at least two neighbors in VG — D. The cardinality of a smallest (largest minimal, respectively) certified dominating set of G is called the certified (upper certified, respectively) domination number of G and is denoted by [formula]), respectively). In this paper relations between domination, upper domination, certified domination and upper certified domination numbers of a graph are studied.
Źródło:: Opuscula Mathematica; 2019, 39, 6; 815-827
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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