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    Tytuł:
    Outer independent rainbow dominating functions in graphs
    Autorzy:
    Mansouri, Zhila
    Mojdeh, Doost Ali
    Powiązania:
    https://bibliotekanauki.pl/articles/1397885.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    outer-independent rainbow domination
    K1
    r -free graphs
    trees
    Opis:
    A 2-rainbow dominating function (2-rD function) of a graph G = (V, E) is a function $ f : V(G) \rightarrow \{ \emptyset, \{1\}, \{2\}, \{1, 2\}\}$ having the property that if $f(x) = \emptyset$, then $f(N(x))= \{1,2\}$. The 2-rainbow domination number $\gamma_{r2}(G)$ is the minimum weight of $ \sum_{v \in V(G)} |f(v)| $ taken over all 2-rainbow dominating functions $f$. An outer-independent 2-rainbow dominating function (OI2-rD function) of a graph G is a 2-rD function $f$ for which the set of all $ v \in V(G)$ with $ f(v)=\emptyset $ is independent. The outer independent 2-rainbow domination number [formula] is the minimum weight of an OI2-rD function of G. In this paper, we study the OI2-rD number of graphs. We give the complexity of the problem OI2-rD of graphs and present lower and upper bounds on $\gamma_{oir2} (G) $. Moreover, we characterize graphs with some small or large OI2-rD numbers and we also bound this parameter from above for trees in terms of the order, leaves and the number of support vertices and characterize all trees attaining the bound. Finally, we show that any ordered pair (a, b) is realizable as the vertex cover number and OI2-rD numbers of some non-trivial tree if and only if $a+1 \leq b \leq 2a $.
    Źródło:
    Opuscula Mathematica; 2020, 40, 5; 599-615
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Roman {2}-Bondage Number of a Graph
    Autorzy:
    Moradi, Ahmad
    Mojdeh, Doost Ali
    Sharifi, Omid
    Powiązania:
    https://bibliotekanauki.pl/articles/32083773.pdf
    Data publikacji:
    2020-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    Roman {2}-domination
    Roman {2}-bondage number
    Opis:
    For a given graph G=(V, E), a Roman {2}-dominating function f : V (G) → {0, 1, 2} has the property that for every vertex u with f(u) = 0, either u is adjacent to a vertex assigned 2 under f, or is adjacent to at least two vertices assigned 1 under f. The Roman {2}-domination number of G, γ{R2}(G), is the minimum of Σu∈V (G) f(u) over all such functions. In this paper, we initiate the study of the problem of finding Roman {2}-bondage number of G. The Roman {2}-bondage number of G, b{R2}, is defined as the cardinality of a smallest edge set E′ ⊆ E for which γ{R2}(G − E′) > γ{R2}(G). We first demonstrate complexity status of the problem by proving that the problem is NP-Hard. Then, we derive useful parametric as well as fixed upper bounds on the Roman {2}-bondage number of G. Specifically, it is known that the Roman bondage number of every planar graph does not exceed 15 (see [S. Akbari, M. Khatirinejad and S. Qajar, A note on the Roman bondage number of planar graphs, Graphs Combin. 29 (2013) 327–331]). We show that same bound will be preserved while computing the Roman {2}-bondage number of such graphs. The paper is then concluded by computing exact value of the parameter for some classes of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 1; 255-268
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Various Bounds for Liar’s Domination Number
    Autorzy:
    Alimadadi, Abdollah
    Mojdeh, Doost Ali
    Rad, Nader Jafari
    Powiązania:
    https://bibliotekanauki.pl/articles/31340859.pdf
    Data publikacji:
    2016-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    liar’s domination
    diameter
    regular graph
    Nordhaus-Gaddum
    Opis:
    Let $ G = (V,E) $ be a graph. A set $ S \subseteq V $ is a dominating set if \( \bigcup_{v \in S} N[v] = V \), where $ N[v] $ is the closed neighborhood of $ v $. Let $ L \subseteq V $ be a dominating set, and let $v$ be a designated vertex in $V$ (an intruder vertex). Each vertex in $ L \cap N[v] $ can report that $v$ is the location of the intruder, but (at most) one $ x \in L \cap N[v] $ can report any $ w \in N[x] $ as the intruder location or $ x $ can indicate that there is no intruder in $ N[x] $. A dominating set $L$ is called a liar’s dominating set if every $ v \in V (G) $ can be correctly identified as an intruder location under these restrictions. The minimum cardinality of a liar’s dominating set is called the liar’s domination number, and is denoted by $ \gamma_{LR} (G) $. In this paper, we present sharp bounds for the liar’s domination number in terms of the diameter, the girth and clique covering number of a graph. We present two Nordhaus-Gaddum type relations for $ \gamma_{LR} (G) $, and study liar’s dominating set sensitivity versus edge-connectivity. We also present various bounds for the liar’s domination component number, that is, the maximum number of components over all minimum liar’s dominating sets.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 3; 629-641
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Further Results on Packing Related Parameters in Graphs
    Autorzy:
    Mojdeh, Doost Ali
    Samadi, Babak
    Yero, Ismael G.
    Powiązania:
    https://bibliotekanauki.pl/articles/32361731.pdf
    Data publikacji:
    2022-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    packing number
    open packing number
    independence number
    Nordhaus-Gaddum inequality
    total domination number
    Opis:
    Given a graph G = (V, E), a set B ⊆ V (G) is a packing in G if the closed neighborhoods of every pair of distinct vertices in B are pairwise disjoint. The packing number ρ(G) of G is the maximum cardinality of a packing in G. Similarly, open packing sets and open packing number are defined for a graph G by using open neighborhoods instead of closed ones. We give several results concerning the (open) packing number of graphs in this paper. For instance, several bounds on these packing parameters along with some Nordhaus-Gaddum inequalities are given. We characterize all graphs with equal packing and independence numbers and give the characterization of all graphs for which the packing number is equal to the independence number minus one. In addition, due to the close connection between the open packing and total domination numbers, we prove a new upper bound on the total domination number γt(T) for a tree T of order n ≥ 2 improving the upper bound γt(T) ≤ (n + s)/2 given by Chellali and Haynes in 2004, in which s is the number of support vertices of T.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 2; 333-348
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New Bounds on the Signed Total Domination Number of Graphs
    Autorzy:
    Moghaddam, Seyyed Mehdi Hosseini
    Mojdeh, Doost Ali
    Samadi, Babak
    Volkmann, Lutz
    Powiązania:
    https://bibliotekanauki.pl/articles/31340895.pdf
    Data publikacji:
    2016-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    open packing
    signed total domination number
    total limited packing
    tuple total domination number
    Opis:
    In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on $ K_{r+1} $-free graphs for $ r \ge 2 $. Applying the concept of total limited packing we bound the signed total domination number of $ G $ with $ \delta (G) \ge 3 $ from above by $ n - 2 \floor{ \frac{ 2 \rho_0 (G) + \delta - 3 }{ 2 } } $. Also, we prove that $ \gamma_{st} (T) \le n − 2(s − s^′ ) $ for any tree $ T $ of order$ $ n, with $ s $ support vertices and $ s^′ $ support vertices of degree two. Moreover, we characterize all trees attaining this bound.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 2; 467-477
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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