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    Wyświetlanie 1-13 z 13
    Tytuł:
    A New Upper Bound for the Perfect Italian Domination Number of a Tree
    Autorzy:
    Nazari-Moghaddam, Sakineh
    Chellali, Mustapha
    Powiązania:
    https://bibliotekanauki.pl/articles/32304138.pdf
    Data publikacji:
    2022-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Italian domination
    Roman domination
    perfect Italian domination
    Opis:
    A perfect Italian dominating function (PIDF) on a graph $G$ is a function $ f : V (G) \rightarrow \{ 0, 1, 2 \} $ satisfying the condition that for every vertex u with $f(u) = 0$, the total weight of $f$ assigned to the neighbors of $u$ is exactly two. The weight of a PIDF is the sum of its functions values over all vertices. The perfect Italian domination number of $G$, denoted $ \gamma_I^p (G) $, is the minimum weight of a PIDF of $G$. In this paper, we show that for every tree $T$ of order $ n \ge 3 $, with $ \mathcal{l} (T) $ leaves and $s(T)$ support vertices, \( \gamma_I^p (T) \ge \tfrac {4n- \mathscr{l}(T) + 2s (T) - 1}{5} \), improving a previous bound given by T.W. Haynes and M.A. Henning in [Perfect Italian domination in trees, Discrete Appl. Math. 260 (2019) 164–177].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 3; 1005-1022
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exact double domination in graphs
    Autorzy:
    Chellali, Mustapha
    Khelladi, Abdelkader
    Maffray, Frédéric
    Powiązania:
    https://bibliotekanauki.pl/articles/744364.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    double domination
    exact double domination
    Opis:
    In a graph a vertex is said to dominate itself and all its neighbours. A doubly dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. A doubly dominating set is exact if every vertex of G is dominated exactly twice. We prove that the existence of an exact doubly dominating set is an NP-complete problem. We show that if an exact double dominating set exists then all such sets have the same size, and we establish bounds on this size. We give a constructive characterization of those trees that admit a doubly dominating set, and we establish a necessary and sufficient condition for the existence of an exact doubly dominating set in a connected cubic graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 3; 291-302
    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-domination in graphs
    Autorzy:
    Chellali, Mustapha
    Mimouni, Malika
    Slater, Peter
    Powiązania:
    https://bibliotekanauki.pl/articles/744569.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    upper locating-domination number
    locating-domination number
    Opis:
    A set D of vertices in a graph G = (V,E) is a locating-dominating set (LDS) if for every two vertices u,v of V-D the sets N(u)∩ D and N(v)∩ D are non-empty and different. The locating-domination number $γ_L(G)$ is the minimum cardinality of a LDS of G, and the upper locating-domination number, $Γ_L(G)$ is the maximum cardinality of a minimal LDS of G. We present different bounds on $Γ_L(G)$ and $γ_L(G)$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2010, 30, 2; 223-235
    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:
    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:
    Extremal Graphs for a Bound on the Roman Domination Number
    Autorzy:
    Bouchou, Ahmed
    Blidia, Mostafa
    Chellali, Mustapha
    Powiązania:
    https://bibliotekanauki.pl/articles/31513493.pdf
    Data publikacji:
    2020-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Roman domination
    Roman domination number
    Nordhaus-Gaddum inequalities
    Opis:
    A Roman dominating function on a graph G = (V, E) is a function f:V (G) → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value w(f) = Σu∈V(G) f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G, denoted by γR(G). In 2009, Chambers, Kinnersley, Prince and West proved that for any graph G with n vertices and maximum degree Δ, γR(G) ≤ n + 1 − Δ. In this paper, we give a characterization of graphs attaining the previous bound including trees, regular and semiregular graphs. Moreover, we prove that the problem of deciding whether γR(G) = n + 1 − Δ is co-complete. Finally, we provide a characterization of extremal graphs of a Nordhaus–Gaddum bound for γR(G) + γR (Ḡ), where Ḡ is the complement graph of G.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 3; 771-785
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Roman Domatic Problem in Graphs and Digraphs: A Survey
    Autorzy:
    Chellali, Mustapha
    Rad, Nader Jafari
    Sheikholeslami, Seyed Mahmoud
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/32304148.pdf
    Data publikacji:
    2022-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Roman domination
    domatic
    Opis:
    In this paper, we survey results on the Roman domatic number and its variants in both graphs and digraphs. This fifth survey completes our works on Roman domination and its variations published in two book chapters and two other surveys.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 3; 861-891
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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:
    On the p-domination number of cactus graphs
    Autorzy:
    Blidia, Mostafa
    Chellali, Mustapha
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/744381.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    p-domination number
    cactus graphs
    Opis:
    Let p be a positive integer and G = (V,E) a graph. A subset S of V is a p-dominating set if every vertex of V-S is dominated at least p times. The minimum cardinality of a p-dominating set a of G is the p-domination number γₚ(G). It is proved for a cactus graph G that γₚ(G) ⩽ (|V| + |Lₚ(G)| + c(G))/2, for every positive integer p ⩾ 2, where Lₚ(G) is the set of vertices of G of degree at most p-1 and c(G) is the number of odd cycles in G.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 3; 355-361
    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:
    Double domination critical and stable graphs upon vertex removal
    Autorzy:
    Khelifi, Soufiane
    Chellali, Mustapha
    Powiązania:
    https://bibliotekanauki.pl/articles/743276.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    double domination
    vertex removal critical graphs
    vertex removal stable graphs
    Opis:
    In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number of G, denoted $γ_{×2}(G)$, is the minimum cardinality among all double dominating sets of G. We consider the effects of vertex removal on the double domination number of a graph. A graph G is $γ_{×2}$-vertex critical graph ($γ_{×2}$-vertex stable graph, respectively) if the removal of any vertex different from a support vertex decreases (does not change, respectively) $γ_{×2}$(G). In this paper we investigate various properties of these graphs. Moreover, we characterize $γ_{×2}$-vertex critical trees and $γ_{×2}$-vertex stable trees.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 4; 643-657
    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 1-13 z 13

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