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    Wyświetlanie 1-13 z 13
    Tytuł:
    The paired-domination and the upper paired-domination numbers of graphs
    Autorzy:
    Ulatowski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/255585.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    paired-domination
    paired-domination number
    upper paired-domination number
    Opis:
    In this paper we continue the study of paired-domination in graphs. A paired-dominating set, abbreviated PDS, of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by γP(G), is the minimum cardinality of a PDS of G. The upper paired-domination number of G, denoted by ΓP(G), is the maximum cardinality of a minimal PDS of G. Let G be a connected graph of order n ≥ 3. Haynes and Slater in [Paired-domination in graphs, Networks 32 (1998), 199-206], showed that γ P(G) ≤ n— 1 and they determine the extremal graphs G achieving this bound. In this paper we obtain analogous results for ΓP(G). Dorbec, Henning and McCoy in [Upper total domination versus upper paired-domination, Questiones Mathematicae 30 (2007), 1-12] determine Γp(Pn), instead in this paper we determine Γp(Cn). Moreover, we describe some families of graphs G for which the equality γP(G) = ΓP(G) holds.
    Źródło:
    Opuscula Mathematica; 2015, 35, 1; 127-135
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    All graphs with paired-domination number two less than their order
    Autorzy:
    Ulatowski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/255220.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    paired-domination
    paired-domination number
    Opis:
    Let G = (V,E) be a graph with no isolated vertices. A set S ⊆ V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number Υρ (G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199–206] Haynes and Slater described graphs G with Υρ (G) = n and also graphs with Υρ (G) = n − 1. In this paper we show all graphs for which Υρ (G) = n − 2.
    Źródło:
    Opuscula Mathematica; 2013, 33, 4; 763-783
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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 ⊆ VG is a dominating set of G if every vertex in VG – 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
    Artykuł
    Tytuł:
    Paired-domination
    Autorzy:
    Fitzpatrick, S.
    Hartnell, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/744199.pdf
    Data publikacji:
    1998
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    paired-domination
    matching
    Opis:
    We are interested in dominating sets (of vertices) with the additional property that the vertices in the dominating set can be paired or matched via existing edges in the graph. This could model the situation of guards or police where each has a partner or backup. This paper will focus on those graphs in which the number of matched pairs of a minimum dominating set of this type equals the size of some maximal matching in the graph. In particular, we characterize the leafless graphs of girth seven or more of this type.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1998, 18, 1; 63-72
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Graphs With Large Semipaired Domination Number
    Autorzy:
    Haynes, Teresa W.
    Henning, Michael A.
    Powiązania:
    https://bibliotekanauki.pl/articles/31343332.pdf
    Data publikacji:
    2019-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    paired-domination
    semipaired domination
    Opis:
    Let $G$ be a graph with vertex set $V$ and no isolated vertices. A subset $ S \subseteq V $ is a semipaired dominating set of $G$ if every vertex in $ V \backslash S $ is adjacent to a vertex in $S$ and $S$ can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number $ \gamma_{pr2}(G) $ is the minimum cardinality of a semipaired dominating set of $G$. We show that if $G$ is a connected graph $G$ of order $ n \ge 3 $, then \( \gamma_{pr2} (G) \le \tfrac{2}{3} n \), and we characterize the extremal graphs achieving equality in the bound.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 3; 659-671
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Total Domination Versus Paired-Domination in Regular Graphs
    Autorzy:
    Cyman, Joanna
    Dettlaff, Magda
    Henning, Michael A.
    Lemańska, Magdalena
    Raczek, Joanna
    Powiązania:
    https://bibliotekanauki.pl/articles/31342314.pdf
    Data publikacji:
    2018-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    total domination
    paired-domination
    Opis:
    A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph induced by S contains a perfect matching, then S is a paired-dominating set. The domination number, denoted γ(G), is the minimum cardinality of a dominating set of G, while the minimum cardinalities of a total dominating set and paired-dominating set are the total domination number, γt(G), and the paired-domination number, γpr(G), respectively. For k ≥ 2, let G be a connected k-regular graph. It is known [Schaudt, Total domination versus paired domination, Discuss. Math. Graph Theory 32 (2012) 435–447] that γpr(G)/γt(G) ≤ (2k)/(k+1). In the special case when k = 2, we observe that γpr(G)/γt(G) ≤ 4/3, with equality if and only if G ≅ C5. When k = 3, we show that γpr(G)/γt(G) ≤ 3/2, with equality if and only if G is the Petersen graph. More generally for k ≥ 2, if G has girth at least 5 and satisfies γpr(G)/γt(G) = (2k)/(k + 1), then we show that G is a diameter-2 Moore graph. As a consequence of this result, we prove that for k ≥ 2 and k ≠ 57, if G has girth at least 5, then γpr(G)/γt(G) ≤ (2k)/(k +1), with equality if and only if k = 2 and G ≅ C5 or k = 3 and G is the Petersen graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 2; 573-586
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Paired- and induced paired-domination in {E,net}-free graphs
    Autorzy:
    Schaudt, Oliver
    Powiązania:
    https://bibliotekanauki.pl/articles/743226.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    paired-domination
    induced paired-domination
    induced matchings
    {E,net}-free graphs
    Opis:
    A dominating set of a graph is a vertex subset that any vertex belongs to or is adjacent to. Among the many well-studied variants of domination are the so-called paired-dominating sets. A paired-dominating set is a dominating set whose induced subgraph has a perfect matching. In this paper, we continue their study.
    We focus on graphs that do not contain the net-graph (obtained by attaching a pendant vertex to each vertex of the triangle) or the E-graph (obtained by attaching a pendant vertex to each vertex of the path on three vertices) as induced subgraphs. This graph class is a natural generalization of {claw, net}-free graphs, which are intensively studied with respect to their nice properties concerning domination and hamiltonicity. We show that any connected {E, net}-free graph has a paired-dominating set that, roughly, contains at most half of the vertices of the graph. This bound is a significant improvement to the known general bounds.
    Further, we show that any {E, net, C₅}-free graph has an induced paired-dominating set, that is a paired-dominating set that forms an induced matching, and that such set can be chosen to be a minimum paired-dominating set. We use these results to obtain a new characterization of {E, net, C₅}-free graphs in terms of the hereditary existence of induced paired-dominating sets. Finally, we show that the induced matching formed by an induced paired-dominating set in a {E, net, C₅}-free graph can be chosen to have at most two times the size of the smallest maximal induced matching possible.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 3; 473-485
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Total domination versus paired domination
    Autorzy:
    Schaudt, Oliver
    Powiązania:
    https://bibliotekanauki.pl/articles/743224.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    total domination
    upper total domination
    paired domination
    upper paired domination
    generalized claw-free graphs
    Opis:
    A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by γₜ. The maximal size of an inclusionwise minimal total dominating set, the upper total domination number, is denoted by Γₜ. A paired dominating set is a dominating set whose induced subgraph has a perfect matching. The minimal size of a paired dominating set, the paired domination number, is denoted by γₚ. The maximal size of an inclusionwise minimal paired dominating set, the upper paired domination number, is denoted by Γₚ.
    In this paper we prove several results on the ratio of these four parameters: For each r ≥ 2 we prove the sharp bound γₚ/γₜ ≤ 2 - 2/r for $K_{1,r}$-free graphs. As a consequence, we obtain the sharp bound γₚ/γₜ ≤ 2 - 2/(Δ+1), where Δ is the maximum degree. We also show for each r ≥ 2 that ${C₅,T_r}$-free graphs fulfill the sharp bound γₚ/γₜ ≤ 2 - 2/r, where $T_r$ is obtained from $K_{1,r}$ by subdividing each edge exactly once. We show that all of these bounds also hold for the ratio Γₚ/Γₜ. Further, we prove that a graph hereditarily has an induced paired dominating set if and only if γₚ ≤ Γₜ holds for any induced subgraph. We also give a finite forbidden subgraph characterization for this condition. We exactly determine the maximal value of the ratio γₚ/Γₜ taken over the induced subgraphs of a graph. As a consequence, we prove for each r ≥ 3 the sharp bound γₚ/Γₜ ≤ 2 - 2/r for graphs that do not contain the corona of $K_{1,r}$ as subgraph. In particular, we obtain the sharp bound γₚ/Γₜ ≤ 2 - 2/Δ.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 3; 435-447
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    γ-paired dominating graphs of cycles
    Autorzy:
    Eakawinrujee, Pannawat
    Trakultraipruk, Nantapath
    Powiązania:
    https://bibliotekanauki.pl/articles/2048671.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    paired dominating graph
    paired dominating set
    paired-domination number
    Opis:
    A paired dominating set of a graph G is a dominating set whose induced subgraph contains a perfect matching. The paired domination number, denoted by γpr(G), is the minimum cardinality of a paired dominating set of G. A γpr(G)-set is a paired dominating set of cardinality γpr(G). The γ-paired dominating graph of G, denoted by PDγ(G), as the graph whose vertices are γpr(G)-sets. Two γpr(G)-sets D1 and D2 are adjacent in PDγ(G) if there exists a vertex u ∈ D1 and a vertex v /∈ D1 such that D2 = (D1 \ {u}) ∪ {v}. In this paper, we present the γ-paired dominating graphs of cycles.
    Źródło:
    Opuscula Mathematica; 2022, 42, 1; 31-54
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Paired domination in prisms of graphs
    Autorzy:
    Mynhardt, Christina
    Schurch, Mark
    Powiązania:
    https://bibliotekanauki.pl/articles/744116.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    paired domination
    prism of a graph
    Cartesian product
    Opis:
    The paired domination number $γ_{pr}(G)$ of a graph G is the smallest cardinality of a dominating set S of G such that ⟨S⟩ has a perfect matching. The generalized prisms πG of G are the graphs obtained by joining the vertices of two disjoint copies of G by |V(G)| independent edges. We provide characterizations of the following three classes of graphs: $γ_{pr}(πG) = 2γ_{pr}(G)$ for all πG; $γ_{pr}(K₂☐ G) = 2γ_{pr}(G)$; $γ_{pr}(K₂☐ G) = γ_{pr}(G)$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 1; 5-23
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Block Graphs with Large Paired Domination Multisubdivision Number
    Autorzy:
    Mynhardt, Christina M.
    Raczek, Joanna
    Powiązania:
    https://bibliotekanauki.pl/articles/32083905.pdf
    Data publikacji:
    2021-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    paired domination
    domination subdivision number
    domination multisubdivision number
    block graph
    Opis:
    The paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 2; 665-684
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
    Autorzy:
    Dettlaff, M.
    Raczek, J.
    Yero, I. G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255785.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    domination
    paired domination
    independent domination
    edge subdivision
    edge multisubdivision
    corona graph
    Opis:
    Given a graph G = (V, E), the subdivision of an edge e = uv ∈ E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision) numbers are denned similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision) numbers of the generalized corona graphs.
    Źródło:
    Opuscula Mathematica; 2016, 36, 5; 575-588
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Neighbourhood total domination in graphs
    Autorzy:
    Arumugam, S.
    Sivagnanam, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/254824.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    neighbourhood total domination
    total domination
    connected domination
    paired domination
    neighbourhood total domatic number
    Opis:
    Let G = (V, E) be a graph without isolated vertices. A dominating set S of G is called a neighbourhood total dominating set (ntd-set) if the induced subgraph ⟨ N(S) ⟩ has no isolated vertices. The minimum cardinality of a ntd-set of G is called the neighbourhood total domination number of G and is denoted by ϒnt(G). The maximum order of a partition of V into ntd-sets is called the neighbourhood total domatic number of G and is denoted by dnt(G). In this paper we initiate a study of these parameters.
    Źródło:
    Opuscula Mathematica; 2011, 31, 4; 519-531
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

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