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    Wyświetlanie 1-8 z 8
    Tytuł:
    Domination Number, Independent Domination Number and 2-Independence Number in Trees
    Autorzy:
    Dehgardi, Nasrin
    Sheikholeslami, Seyed Mahmoud
    Valinavaz, Mina
    Aram, Hamideh
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/32083746.pdf
    Data publikacji:
    2021-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    2-independence number
    domination number
    independent domination number
    Opis:
    For a graph $G$, let $\gamma(G)$ be the domination number, $i(G)$ be the independent domination number and $\beta_2(G)$ be the 2-independence number. In this paper, we prove that for any tree $T$ of order $n ≥ 2, 4\beta_2(T) − 3\gamma(T) ≥ 3i(T)$, and we characterize all trees attaining equality. Also we prove that for every tree $T$ of order \(n ≥ 2, i(T)≤\frac{3\beta_2(T)}{4}\), and we characterize all extreme trees.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 1; 39-49
    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 Co-Roman Domination in Graphs
    Autorzy:
    Shao, Zehui
    Sheikholeslami, Seyed Mahmoud
    Soroudi, Marzieh
    Volkmann, Lutz
    Liu, Xinmiao
    Powiązania:
    https://bibliotekanauki.pl/articles/31343438.pdf
    Data publikacji:
    2019-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    co-Roman dominating function
    co-Roman domination number
    Roman domination
    Opis:
    Let $G = (V, E)$ be a graph and let $f : V (G) \rightarrow {0, 1, 2}$ be a function. A vertex $v$ is said to be protected with respect to $f$, if $f(v) > 0$ or $f(v) = 0$ and $v$ is adjacent to a vertex of positive weight. The function $f$ is a co-Roman dominating function if (i) every vertex in $V$ is protected, and (ii) each $ v \in V $ with positive weight has a neighbor $ u \in V $ with $ f(u) = 0 $ such that the function $ f_{uv} : V \rightarrow {0, 1, 2} $, defined by $ f_{uv} (u) = 1$, $ f_{uv}(v) = f(v) − 1$ and $ f_{uv}(x) = f(x)$ for $ x \in V \backslash \{ v, u \} $, has no unprotected vertex. The weight of $f$ is $ \omega(f) = \Sigma_{ v \in V } f(v) $. The co-Roman domination number of a graph $G$, denoted by $ \gamma_{cr}(G) $, is the minimum weight of a co-Roman dominating function on $G$. In this paper, we give a characterization of graphs of order $n$ for which co-Roman domination number is \( \tfrac{2n}{3} \) or $n − 2$, which settles two open problem in [S. Arumugam, K. Ebadi and M. Manrique, Co-Roman domination in graphs, Proc. Indian Acad. Sci. Math. Sci. 125 (2015) 1–10]. Furthermore, we present some sharp bounds on the co-Roman domination number.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 2; 455-472
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Distance Roman Domination Numbers of Graphs
    Autorzy:
    Aram, Hamideh
    Norouzian, Sepideh
    Sheikholeslami, Seyed Mahmoud
    Powiązania:
    https://bibliotekanauki.pl/articles/30098151.pdf
    Data publikacji:
    2013-09-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    k-distance Roman dominating function
    k-distance Roman domination number
    Roman dominating function
    Roman domination number
    Opis:
    Let $ k $ be a positive integer, and let $ G $ be a simple graph with vertex set $ V (G) $. A k-distance Roman dominating function on $ G $ is a labeling $ f : V (G) → {0, 1, 2} $ such that for every vertex with label 0, there is a vertex with label 2 at distance at most $ k $ from each other. The weight of a $k$-distance Roman dominating function $ f $ is the value $ \omega (f) =∑_{v∈V} f(v) $. The k-distance Roman domination number of a graph $G$, denoted by $\gamma_R^k (D) $, equals the minimum weight of a $k$-distance Roman dominating function on G. Note that the 1-distance Roman domination number $ \gamma_R^1 (G) $ is the usual Roman domination number $ \gamma_R (G) $. In this paper, we investigate properties of the $k$-distance Roman domination number. In particular, we prove that for any connected graph $ G $ of order $ n \geq k +2$, $\gamma_R^k (G) \leq 4n//(2k +3) $ and we characterize all graphs that achieve this bound. Some of our results extend these ones given by Cockayne et al. in 2004 and Chambers et al. in 2009 for the Roman domination number.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 4; 717-730
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On The Total Roman Domination in Trees
    Autorzy:
    Amjadi, Jafar
    Sheikholeslami, Seyed Mahmoud
    Soroudi, Marzieh
    Powiązania:
    https://bibliotekanauki.pl/articles/31343413.pdf
    Data publikacji:
    2019-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    total Roman dominating function
    total Roman domination number
    trees
    Opis:
    A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex. The weight of a total Roman dominating function f is the value f(V (G)) = Σu∈V(G) f(u). The total Roman domination number γtR(G) is the minimum weight of a total Roman dominating function of G. Ahangar et al. in [H.A. Ahangar, M.A. Henning, V. Samodivkin and I.G. Yero, Total Roman domination in graphs, Appl. Anal. Discrete Math. 10 (2016) 501–517] recently showed that for any graph G without isolated vertices, 2γ(G) ≤ γtR(G) ≤ 3γ(G), where γ(G) is the domination number of G, and they raised the problem of characterizing the graphs G achieving these upper and lower bounds. In this paper, we provide a constructive characterization of these trees.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 2; 519-532
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Signed Total Roman Edge Domination In Graphs
    Autorzy:
    Asgharsharghi, Leila
    Sheikholeslami, Seyed Mahmoud
    Powiązania:
    https://bibliotekanauki.pl/articles/31341578.pdf
    Data publikacji:
    2017-11-27
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed total Roman dominating function
    signed total Roman domination number
    signed total Roman edge dominating function
    signed total Roman edge domination number
    Opis:
    Let $ G = (V,E) $ be a simple graph with vertex set $V$ and edge set $E$. A signed total Roman edge dominating function of $G$ is a function $ f : E \rightarrow {−1, 1, 2} $ satisfying the conditions that (i) $ \Sigma_{e^′ \in N(e)} f(e^′) \ge 1 $ for each $ e \in E $, where $N(e)$ is the open neighborhood of $e$, and (ii) every edge $e$ for which $f(e) = −1$ is adjacent to at least one edge $ e^′$ for which $f(e^′) = 2$. The weight of a signed total Roman edge dominating function $f$ is $ \omega(f) = \Sigma_{e \in E } f(e) $. The signed total Roman edge domination number $ \gamma_{stR}^' (G) $ of $G$ is the minimum weight of a signed total Roman edge dominating function of $G$. In this paper, we first prove that for every tree $T$ of order $ n \ge 4 $, $ \gamma_{stR}^' (T) \ge \frac{17−2n}{5} $ and we characterize all extreme trees, and then we present some sharp bounds for the signed total Roman edge domination number. We also determine this parameter for some classes of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 4; 1039-1053
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Signed Roman Edge k -Domination in Graphs
    Autorzy:
    Asgharsharghi, Leila
    Sheikholeslami, Seyed Mahmoud
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31342188.pdf
    Data publikacji:
    2017-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signed Roman edge k -dominating function
    signed Roman edge k -domination number
    Opis:
    Let $ k \ge 1 $ be an integer, and $ G = (V, E) $ be a finite and simple graph. The closed neighborhood $ N_G [e]$ of an edge $e$ in a graph $G$ is the set consisting of $e$ and all edges having a common end-vertex with $e$. A signed Roman edge $k$-dominating function (SREkDF) on a graph $G$ is a function $ f : E \rightarrow {−1, 1, 2} $ satisfying the conditions that (i) for every edge $e$ of $G$, $ \Sigma_{ x \in N_G [e] } f(x) \ge k $ and (ii) every edge e for which $f(e) = −1$ is adjacent to at least one edge $ e^′ $ for which $ f(e^′) = 2 $. The minimum of the values $ \Sigma_{e \in E} f(e) $, taken over all signed Roman edge $k$-dominating functions $f$ of $G$ is called the signed Roman edge $k$-domination number of $G$, and is denoted by $ \gamma_{sRk}^' (G) $. In this paper we initiate the study of the signed Roman edge $k$-domination in graphs and present some (sharp) bounds for this parameter.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 1; 39-53
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The k-Rainbow Bondage Number of a Digraph
    Autorzy:
    Amjadi, Jafar
    Mohammadi, Negar
    Sheikholeslami, Seyed Mahmoud
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31339490.pdf
    Data publikacji:
    2015-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    k-rainbow dominating function
    k-rainbow domination number
    k-rainbow bondage number
    digraph
    Opis:
    Let $ D = (V,A) $ be a finite and simple digraph. A $k$-rainbow dominating function ($ k \text{RDF} $) of a digraph $D$ is a function $f$ from the vertex set $V$ to the set of all subsets of the set ${1, 2, . . ., k}$ such that for any vertex $ v \in V $ with $ f(v) = \emptyset $ the condition \( \bigcup_{ u \in N^−(v) } f(u) = {1, 2, . . ., k} \) is fulfilled, where $ N^− (v) $ is the set of in-neighbors of $v$. The weight of a \( k \text{RDF} \) \( f \) is the value \( \omega (f) = \sum_{v \in V} |f(v)| \). The $k$-rainbow domination number of a digraph $D$, denoted by $ \gamma_{rk} (D) $, is the minimum weight of a $ k \text{RDF} $ of $D$. The $k$-rainbow bondage number $ b_{rk} (D) $ of a digraph $D$ with maximum in-degree at least two, is the minimum cardinality of all sets $ A^\prime \subseteq A $ for which $ \gamma_{rk} (D−A^\prime ) > \gamma_{rk} (D) $. In this paper, we establish some bounds for the $k$-rainbow bondage number and determine the $k$-rainbow bondage number of several classes of digraphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2015, 35, 2; 261-270
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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