Informacja

Drogi użytkowniku, aplikacja do prawidłowego działania wymaga obsługi JavaScript. Proszę włącz obsługę JavaScript w Twojej przeglądarce.

English (EN)·Polski (PL)·Yкраїнський (UK)
Przejdź do strony domowej biblioteki Centralna Biblioteka Wojskowa Link otwiera się w nowym oknie Logo biblioteki Prolib Integro - strona głównaCentralna Biblioteka Wojskowa

Wyszukujesz frazę "DOMINATION" wg kryterium: Temat

  Lista filtrów
Wyrównaj
    Wyświetlanie 1-10 z 10
    Tytuł:
    A note on a relation between the weak and strong domination numbers of a graph
    Autorzy:
    Boutrig, R.
    Chellali, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255983.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    weak domination
    strong domination
    Opis:
    In a graph G = (V, E) a vertex is said to dominate itself and all its neighbors. A set D ⊆ V is a weak (strong, respectively) dominating set of G if every vertex v ∈ V - S is adjacent to a vertex u ∈ D such that dG(v) ≥ dG(u) (dG(v) ≤ dG(u), respectively). The weak (strong, respectively) domination number of G, denoted by ϒw(G) (ϒs(G), respectively), is the minimum cardinality of a weak (strong, respectively) dominating set of G. In this note we show that if G is a connected graph of order n ≥ 3, then ϒw(G) + tϒs(G) ≤ n, where t = 3/(Δ+1) if G is an arbitrary graph, t = 3/5 if G is a block graph, and t = 2/3 if G is a claw free graph.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 235-238
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Total Roman {2}-Dominating Functions in Graphs
    Autorzy:
    Ahangar, H. Abdollahzadeh
    Chellali, M.
    Sheikholeslami, S.M.
    Valenzuela-Tripodoro, J.C.
    Powiązania:
    https://bibliotekanauki.pl/articles/32304142.pdf
    Data publikacji:
    2022-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Roman domination
    Roman {2}-domination
    total Roman {2}-domination
    Opis:
    A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for every vertex v ∈ V with f(v) = 0 there is a neighbor u of v with f(u) = 2, or there are two neighbors x, y of v with f(x) = f(y) = 1. A total Roman {2}-dominating function (TR2DF) is an R2F f such that the set of vertices with f(v) > 0 induce a subgraph with no isolated vertices. The weight of a TR2DF is the sum of its function values over all vertices, and the minimum weight of a TR2DF of G is the total Roman {2}-domination number γtR2(G). In this paper, we initiate the study of total Roman {2}-dominating functions, where properties are established. Moreover, we present various bounds on the total Roman {2}-domination number. We also show that the decision problem associated with γtR2(G) is possible to compute this parameter in linear time for bounded clique-width graphs (including trees).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 3; 937-958
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on the independent Roman domination in unicyclic graphs
    Autorzy:
    Chellali, M.
    Rad, N. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255989.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Roman domination
    independent Roman domination
    strong equality
    Opis:
    A Roman dominating function (RDF) on a graph G= (V, E) is a function ƒ : V → {0, 1, 2} satisfying the condition that every vertex u for which ƒ(u) = 0 is adjacent to at least one vertex v for which ƒ(v)=2. The weight of an RDF is the value [formula]. An RDF ƒ in a graph G is independent if no two vertices assigned positive values are adjacent. The Roman domination number ΥR (G) (respectively, the independent Roman domination number ΥR(G) is the minimum weight of an RDF (respectively, independent RDF) on G. We say that ΥR(G) strongly equals iR(G), denoted by ΥR(G) ≡ iR(G), if every RDF on G of minimum weight is independent. In this note we characterize all unicyclic graphs G with ΥR(G) ≡ iR(G).
    Źródło:
    Opuscula Mathematica; 2012, 32, 4; 715-718
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bounds on the 2-domination number in cactus graphs
    Autorzy:
    Chellali, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/254915.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    2-domination number
    total domination number
    independence number
    cactus graphs
    trees
    Opis:
    A 2-dominating set of a graph G is a set D of vertices of G such that every vertex not in S is dominated at least twice. The minimum cardinality of a 2-dominating set of G is the 2-domination number γ2(G). We show that if G is a nontrivial connected cactus graph with k(G) even cycles (k(G) ≥ 0), then γ2(G) ≥ γt(G) - k(G), and if G is a graph of order n with at most one cycle, then γ2(G) ≥ (n + l - s)/2 improving Fink and Jacobson's lower bound for trees with l > s, where γt(G), l and s are the total domination number, the number of leaves and support vertices of G, respectively. We also show that if T is a tree of order n ≥ 3, then γ2(T) ≤ β(T) + s - 1, where β(T) is the independence number of T.
    Źródło:
    Opuscula Mathematica; 2006, 26, 1; 5-12
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on k-Roman graphs
    Autorzy:
    Bouchou, A.
    Blidia, M.
    Chellali, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255821.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Roman k-domination
    k-Roman graph
    Opis:
    Let G = (V,E) be a graph and let k be a positive integer. A subset D of V (G) is a k-dominating set of G if every vertex in V (G) \D has at least k neighbours in D. The k-domination number Υk(G) is the minimum cardinality of a k-dominating set of G. A Roman k-dominating function on G is a function f : V (G) →{0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices v1, v2, . . . , vk with f(vi) = 2 for i = 1, 2, . . . , k. The weight of a Roman k-dominating function is the value [formula] and the minimum weight of a Roman k-dominating function on G is called the Roman k-domination number Υk(G) of G. A graph G is said to be a k-Roman graph if ΥkR(G) = 2Υk(G) . In this note we study k-Roman graphs.
    Źródło:
    Opuscula Mathematica; 2013, 33, 4; 641-646
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the global offensive alliance number of a tree
    Autorzy:
    Bouzefrane, M.
    Chellali, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255263.pdf
    Data publikacji:
    2009
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    global offensive alliance number
    domination number
    trees
    Opis:
    For a graph G = (V, E), a set S ⊆ V is a dominating set if every vertex in V - S has at least a neighbor in S. A dominating set S is a global offensive alliance if for every vertex v in V - S, at least half of the vertices in its closed neighborhood are in S. The domination number ϒ(G) is the minimum cardinality of a dominating set of G and the global offensive alliance number ϒo(G) is the minimum cardinality of a global offensive alliance of G. We first show that every tree of order at least three with l leaves and s support vertices satisfies ϒo(T) ≥ (n - l + s + 1)/3 and we characterize extremal trees attaining this lower bound. Then we give a constructive characterization of trees with equal domination and global offensive alliance numbers.
    Źródło:
    Opuscula Mathematica; 2009, 29, 3; 223-228
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Total 2-Rainbow Domination Numbers of Trees
    Autorzy:
    Ahangar, H. Abdollahzadeh
    Amjadi, J.
    Chellali, M.
    Nazari-Moghaddam, S.
    Sheikholeslami, S.M.
    Powiązania:
    https://bibliotekanauki.pl/articles/32083855.pdf
    Data publikacji:
    2021-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    2-rainbow dominating function
    2-rainbow domination number
    total 2-rainbow dominating function
    total 2-rainbow domination number
    Opis:
    A 2-rainbow dominating function (2RDF) of a graph $G = (V(G), E(G))$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set {1, 2} such that for every vertex $v ∈ V(G)$ with $f(v) = ∅$ the condition \(\bigcup_{u∈N(v)}f(u) = \{1, 2\}\) is fulfilled, where $N(v)$ is the open neighborhood of $v$. A total 2-rainbow dominating function $f$ of a graph with no isolated vertices is a 2RDF with the additional condition that the subgraph of $G$ induced by $\{v ∈ V (G) | f(v) ≠∅\}$ has no isolated vertex. The total 2-rainbow domination number, $\gamma_{tr2}(G)$, is the minimum weight of a total 2-rainbow dominating function of $G$. In this paper, we establish some sharp upper and lower bounds on the total 2-rainbow domination number of a tree. Moreover, we show that the decision problem associated with $\gamma_{tr2}(G)$ is NP-complete for bipartite and chordal graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 2; 345-364
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on global alliances in trees
    Autorzy:
    Bouzefrane, M.
    Chellali, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/254977.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    global defensive alliance
    global offensive alliance
    domination
    trees
    Opis:
    For a graph G = (V,E), a set S ⊆ V is a dominating set if every vertex in V - S has at least a neighbor in S. A dominating set S is a global offensive (respectively, defensive) alliance if for each vertex in V - S (respectively, in S) at least half the vertices from the closed neighborhood of v are in S. The domination number γ (G) is the minimum cardinality of a dominating set of G, and the global offensive alliance number γo(G) (respectively, global defensive alliance number γa(G)) is the minimum cardinality of a global offensive alliance (respectively, global deffensive alliance) of G. We show that if T is a tree of order n, then γo(T) ≤ 2γ (T) - 1 and if n ≥ 3, then γo(T) ≤ 3/2?a(T) ? 1. Moreover, all extremal trees attaining the first bound are characterized.
    Źródło:
    Opuscula Mathematica; 2011, 31, 2; 153-159
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Total Roman Reinforcement in Graphs
    Autorzy:
    Ahangar, H. Abdollahzadeh
    Amjadi, J.
    Chellali, M.
    Nazari-Moghaddam, S.
    Sheikholeslami, S.M.
    Powiązania:
    https://bibliotekanauki.pl/articles/31343238.pdf
    Data publikacji:
    2019-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    total Roman domination number
    total Roman reinforcement number
    Opis:
    A total Roman dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex. The minimum weight of a total Roman dominating function on a graph G is called the total Roman domination number of G. The total Roman reinforcement number rtR(G) of a graph G is the minimum number of edges that must be added to G in order to decrease the total Roman domination number. In this paper, we investigate the proper- ties of total Roman reinforcement number in graphs, and we present some sharp bounds for rtR(G). Moreover, we show that the decision problem for total Roman reinforcement is NP-hard for bipartite graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 4; 787-803
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Trees with equal global offensive k-alliance and k-domination numbers
    Autorzy:
    Chellali, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255451.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    global offensive k-alliance number
    k-domination number
    trees
    Opis:
    Let k ≥ 1 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if |N(v) ∩ S| ≥ |N(v) - S| + k for every v ∈ V (G) - S, where N(v) is the neighborhood of v. The subset S is a k-dominating set of G if every vertex in V (G) - S has at least k neighbors in S. The global offensive k-alliance number [formula] is the minimum cardinality of a global offensive k-alliance in G and the k-domination number ϒ k(G) is the minimum cardinality of a k-dominating set of G. For every integer k ≥ 1 every graph G satisfies [formula]. In this paper we provide for k ≥ 2 a characterization of trees T with equal [formula] and ϒ k(T).
    Źródło:
    Opuscula Mathematica; 2010, 30, 3; 249-254
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

      Ta witryna wykorzystuje pliki cookies do przechowywania informacji na Twoim komputerze. Pliki cookies stosujemy w celu świadczenia usług na najwyższym poziomie, w tym w sposób dostosowany do indywidualnych potrzeb. Korzystanie z witryny bez zmiany ustawień dotyczących cookies oznacza, że będą one zamieszczane w Twoim komputerze. W każdym momencie możesz dokonać zmiany ustawień dotyczących cookies