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Wyszukujesz frazę "total {k}-domination number" wg kryterium: Temat

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    Wyświetlanie 1-6 z 6
    Tytuł:
    The total {k}-domatic number of digraphs
    Autorzy:
    Sheikholeslami, Seyed
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/743233.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    digraph
    total {k}-dominating function
    total {k}-domination number
    total {k}-domatic number
    Opis:
    For a positive integer k, a total {k}-dominating function of a digraph D is a function f from the vertex set V(D) to the set {0,1,2, ...,k} such that for any vertex v ∈ V(D), the condition $∑_{u ∈ N^{ -}(v)}f(u) ≥ k$ is fulfilled, where N¯(v) consists of all vertices of D from which arcs go into v. A set ${f₁,f₂, ...,f_d}$ of total {k}-dominating functions of D with the property that $∑_{i = 1}^d f_i(v) ≤ k$ for each v ∈ V(D), is called a total {k}-dominating family (of functions) on D. The maximum number of functions in a total {k}-dominating family on D is the total {k}-domatic number of D, denoted by $dₜ^{{k}}(D)$. Note that $dₜ^{{1}}(D)$ is the classic total domatic number $dₜ(D)$. In this paper we initiate the study of the total {k}-domatic number in digraphs, and we present some bounds for $dₜ^{{k}}(D)$. Some of our results are extensions of well-know properties of the total domatic number of digraphs and the total {k}-domatic number of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 3; 461-471
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the total k-domination number of graphs
    Autorzy:
    Kazemi, Adel
    Powiązania:
    https://bibliotekanauki.pl/articles/743228.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    total k-domination (k-tuple total domination) number
    k-tuple domination number
    k-transversal number
    Opis:
    Let k be a positive integer and let G = (V,E) be a simple graph. The k-tuple domination number $γ_{×k}(G)$ of G is the minimum cardinality of a k-tuple dominating set S, a set that for every vertex v ∈ V, $|N_G[v] ∩ S| ≥ k$. Also the total k-domination number $γ_{×k,t}(G)$ of G is the minimum cardinality of a total k -dominating set S, a set that for every vertex v ∈ V, $|N_G(v) ∩ S| ≥ k$. The k-transversal number τₖ(H) of a hypergraph H is the minimum size of a subset S ⊆ V(H) such that |S ∩e | ≥ k for every edge e ∈ E(H).
    We know that for any graph G of order n with minimum degree at least k, $γ_{×k}(G) ≤ γ_{×k,t}(G) ≤ n$. Obviously for every k-regular graph, the upper bound n is sharp. Here, we give a sufficient condition for $γ_{×k,t}(G) < n$. Then we characterize complete multipartite graphs G with $γ_{×k}(G) = γ_{×k,t}(G)$. We also state that the total k-domination number of a graph is the k -transversal number of its open neighborhood hypergraph, and also the domination number of a graph is the transversal number of its closed neighborhood hypergraph. Finally, we give an upper bound for the total k -domination number of the cross product graph G×H of two graphs G and H in terms on the similar numbers of G and H. Also, we show that this upper bound is strict for some graphs, when k = 1.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 3; 419-426
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Upper Bounds on the Signed Total (k, k)-Domatic Number of Graphs
    Autorzy:
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31339301.pdf
    Data publikacji:
    2015-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed total (k
    k)-domatic number
    signed total k-dominating function
    signed total k-domination number
    regular graphs
    Opis:
    Let $G$ be a graph with vertex set $V (G)$, and let $ f : V (G) \rightarrow {−1, 1}$ be a two-valued function. If $ k \geq 1$ is an integer and \( \sum_{ x \in N(v)} f(x) \geq k \) for each $ v \in V (G) $, where $N(v)$ is the neighborhood of $v$, then $f$ is a signed total $k$-dominating function on $G$. A set ${f_1, f_2, . . ., f_d}$ of distinct signed total k-dominating functions on $G$ with the property that \( \sum_{i=1}^d f_i(x) \leq k \) for each $ x \in V (G)$, is called a signed total ($k$, $k$)-dominating family (of functions) on $G$. The maximum number of functions in a signed total ($k$, $k$)-dominating family on $G$ is the signed total ($k$, $k$)-domatic number of $G$. In this article we mainly present upper bounds on the signed total ($k$, $k$)- domatic number, in particular for regular graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2015, 35, 4; 641-650
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on bipartite graphs whose [1, k]-domination number equal to their number of vertices
    Autorzy:
    Ghareghani, Narges
    Peterin, Iztok
    Sharifani, Pouyeh
    Powiązania:
    https://bibliotekanauki.pl/articles/256007.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    domination
    [1, k]-domination number
    [l,k]-total domination number
    bipartite graphs
    Opis:
    A subset D of the vertex set V of a graph G is called an [1, k]-dominating set if every vertex from V — D is adjacent to at least one vertex and at most fc vertices of D. A [1, k]-dominating set with the minimum number of vertices is called a [formula]-set and the number of its vertices is the [1, k]-domination number [formula] of G. In this short note we show that the decision problem whether [formula] is an NP-hard problem, even for bipartite graphs. Also, a simple construction of a bipartite graph G of order n satisfying [formula] is given for every integer n ≥ (k + l)(2k + 3).
    Źródło:
    Opuscula Mathematica; 2020, 40, 3; 375-382
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Signed Total Roman k-Domatic Number Of A Graph
    Autorzy:
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31341581.pdf
    Data publikacji:
    2017-11-27
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed total Roman k-dominating function
    signed total Roman k-domination number
    signed total Roman k-domatic number
    Opis:
    Let $ k \ge 1 $ be an integer. A signed total Roman $k$-dominating function on a graph $G$ is a function $ f : V (G) \rightarrow {−1, 1, 2} $ such that $ \Sigma_{ u \in N(v) } f(u) \ge k $ for every $ v \in V (G) $, where $ N(v) $ is the neighborhood of $ v $, and every vertex $ u \in V (G) $ for which $ f(u) = −1 $ is adjacent to at least one vertex w for which $ f(w) = 2 $. A set $ { f_1, f_2, . . ., f_d} $ of distinct signed total Roman $k$-dominating functions on $G$ with the property that $ \Sigma_{i=1}^d f_i(v) \le k $ for each $ v \in V (G) $, is called a signed total Roman $k$-dominating family (of functions) on $G$. The maximum number of functions in a signed total Roman $k$-dominating family on $G$ is the signed total Roman $k$-domatic number of $G$, denoted by $ d_{stR}^k (G) $. In this paper we initiate the study of signed total Roman $k$-domatic numbers in graphs, and we present sharp bounds for $ d_{stR}^k (G) $. In particular, we derive some Nordhaus-Gaddum type inequalities. In addition, we determine the signed total Roman $k$-domatic number of some graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 4; 1027-1038
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the inverse signed total domination number in graphs
    Autorzy:
    Mojdeh, D. A.
    Samadi, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/255392.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    inverse signed total dominating function
    inverse signed total domination number
    k-tuple total domination number
    Opis:
    In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on Kr+1-free graphs for r ≥ 2. Also, we bound this parameter for a tree from below in terms of its order and the number of leaves and characterize all trees attaining this bound.
    Źródło:
    Opuscula Mathematica; 2017, 37, 3; 447-456
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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