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Wyszukujesz frazę "trees" wg kryterium: Temat


Wyświetlanie 1-6 z 6
Tytuł:
On the dominator colorings in trees
Autorzy:
Merouane, Houcine
Chellali, Mustapha
Powiązania:
https://bibliotekanauki.pl/articles/743280.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominator coloring
domination
trees
Opis:
In a graph G, a vertex is said to dominate itself and all its neighbors. A dominating set of a graph G is a subset of vertices that dominates every vertex of G. The domination number γ(G) is the minimum cardinality of a dominating set of G. A proper coloring of a graph G is a function from the set of vertices of the graph to a set of colors such that any two adjacent vertices have different colors. A dominator coloring of a graph G is a proper coloring such that every vertex of V dominates all vertices of at least one color class (possibly its own class). The dominator chromatic number $χ_d(G)$ is the minimum number of color classes in a dominator coloring of G. Gera showed that every nontrivial tree T satisfies $γ(T)+1 ≤ χ_d(T) ≤ γ(T)+2$. In this note we characterize nontrivial trees T attaining each bound.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 4; 677-683
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Characterization of trees with equal 2-domination number and domination number plus two
Autorzy:
Chellali, Mustapha
Volkmann, Lutz
Powiązania:
https://bibliotekanauki.pl/articles/743587.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
2-domination number
domination number
trees
Opis:
Let G = (V(G),E(G)) be a simple graph, and let k be a positive integer. A subset D of V(G) is a k-dominating set if every vertex of V(G) - D is dominated at least k times by D. The k-domination number γₖ(G) is the minimum cardinality of a k-dominating set of G. In [5] Volkmann showed that for every nontrivial tree T, γ₂(T) ≥ γ₁(T)+1 and characterized extremal trees attaining this bound. In this paper we characterize all trees T with γ₂(T) = γ₁(T)+2.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 4; 687-697
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On locating and differentiating-total domination in trees
Autorzy:
Chellali, Mustapha
Powiązania:
https://bibliotekanauki.pl/articles/743043.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
locating-total domination
differentiating-total domination
trees
Opis:
A total dominating set of a graph G = (V,E) with no isolated vertex is a set S ⊆ V such that every vertex is adjacent to a vertex in S. A total dominating set S of a graph G is a locating-total dominating set if for every pair of distinct vertices u and v in V-S, N(u)∩S ≠ N(v)∩S, and S is a differentiating-total dominating set if for every pair of distinct vertices u and v in V, N[u]∩S ≠ N[v] ∩S. Let $γₜ^L(G)$ and $γₜ^D(G)$ be the minimum cardinality of a locating-total dominating set and a differentiating-total dominating set of G, respectively. We show that for a nontrivial tree T of order n, with l leaves and s support vertices, $γₜ^L(T) ≥ max{2(n+l-s+1)/5,(n+2-s)/2}$, and for a tree of order n ≥ 3, $γₜ^D(T) ≥ 3(n+l-s+1)/7$, improving the lower bounds of Haynes, Henning and Howard. Moreover we characterize the trees satisfying $γₜ^L(T) = 2(n+l- s+1)/5$ or $γₜ^D(T) = 3(n+l-s+1)/7$.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 3; 383-392
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Trees with equal 2-domination and 2-independence numbers
Autorzy:
Chellali, Mustapha
Meddah, Nacéra
Powiązania:
https://bibliotekanauki.pl/articles/743338.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
2-domination number
2-independence number
trees
Opis:
Let G = (V,E) be a graph. A subset S of V is a 2-dominating set if every vertex of V-S is dominated at least 2 times, and S is a 2-independent set of G if every vertex of S has at most one neighbor in S. The minimum cardinality of a 2-dominating set a of G is the 2-domination number γ₂(G) and the maximum cardinality of a 2-independent set of G is the 2-independence number β₂(G). Fink and Jacobson proved that γ₂(G) ≤ β₂(G) for every graph G. In this paper we provide a constructive characterization of trees with equal 2-domination and 2-independence numbers.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 2; 263-270
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees
Autorzy:
Chellali, Mustapha
Rad, Nader Jafari
Powiązania:
https://bibliotekanauki.pl/articles/30146596.pdf
Data publikacji:
2013-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Roman domination
independent Roman domination
strong equality
trees
Opis:
A Roman dominating function (RDF) on a graph $G = (V,E)$ is a function $ f : V \rightarrow {0, 1, 2} $ satisfying the condition that every vertex $ u $ for which $ f(u) = 0 $ is adjacent to at least one vertex $v$ for which $f(v) = 2$. The weight of an RDF is the value $ f(V (G)) = \Sigma_{u \in V (G) } f(u) $. An RDF $f$ in a graph $G$ is independent if no two vertices assigned positive values are adjacent. The Roman domination number $ \gamma_R (G) $ (respectively, the independent Roman domination number $ i_R(G) $) is the minimum weight of an RDF (respectively, independent RDF) on $G$. We say that $ \gamma_R(G)$ strongly equals $ i_R(G)$, denoted by $ \gamma_R (G) \equiv i_R(G)$, if every RDF on $G$ of minimum weight is independent. In this paper we provide a constructive characterization of trees $T$ with $ \gamma_R(T) \equiv i_R(T) $.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 2; 337-346
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global alliances and independence in trees
Autorzy:
Chellali, Mustapha
Haynes, Teresa
Powiązania:
https://bibliotekanauki.pl/articles/743643.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
defensive alliance
offensive alliance
global alliance
domination
trees
independence number
Opis:
A global defensive (respectively, offensive) alliance in a graph G = (V,E) is a set of vertices S ⊆ V with the properties that every vertex in V-S has at least one neighbor in S, and for each vertex v in S (respectively, in V-S) at least half the vertices from the closed neighborhood of v are in S. These alliances are called strong if a strict majority of vertices from the closed neighborhood of v must be in S. For each kind of alliance, the associated parameter is the minimum cardinality of such an alliance. We determine relationships among these four parameters and the vertex independence number for trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 1; 19-27
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-6 z 6

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