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    Wyświetlanie 1-9 z 9
    Tytuł:
    Nordhaus-Gaddum bounds for upper total domination
    Autorzy:
    Haynes, Teresa W.
    Henning, Michael A.
    Powiązania:
    https://bibliotekanauki.pl/articles/2216175.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    upper total domination
    Nordhaus-Gaddum bound
    Opis:
    A set S of vertices in an isolate-free graph G is a total dominating set if every vertex in G is adjacent to a vertex in S. A total dominating set of G is minimal if it contains no total dominating set of $\bar{G}$ as a proper subset. The upper total domination number $Γ_t(G)$ of G is the maximum cardinality of a minimal total dominating set in G. We establish Nordhaus-Gaddum bounds involving the upper total domination numbers of a graph G and its complement $\bar{G}$. We prove that if G is a graph of order n such that both G and $\bar{G}$ are isolate-free, then $Γ_t(G) + Γ_t(\bar{G}) ≤ n + 2$ and $Γ_t(G)Γ_t(\bar{G}) ≤ 1/4 (n + 2)^2$, and these bounds are tight.
    Źródło:
    Opuscula Mathematica; 2022, 42, 4; 573-582
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Graphs With Large Semipaired Domination Number
    Autorzy:
    Haynes, Teresa W.
    Henning, Michael A.
    Powiązania:
    https://bibliotekanauki.pl/articles/31343332.pdf
    Data publikacji:
    2019-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    paired-domination
    semipaired domination
    Opis:
    Let $G$ be a graph with vertex set $V$ and no isolated vertices. A subset $ S \subseteq V $ is a semipaired dominating set of $G$ if every vertex in $ V \backslash S $ is adjacent to a vertex in $S$ and $S$ can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number $ \gamma_{pr2}(G) $ is the minimum cardinality of a semipaired dominating set of $G$. We show that if $G$ is a connected graph $G$ of order $ n \ge 3 $, then \( \gamma_{pr2} (G) \le \tfrac{2}{3} n \), and we characterize the extremal graphs achieving equality in the bound.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 3; 659-671
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    1-Restricted Optimal Rubbling on Graphs
    Autorzy:
    Beeler, Robert A.
    Haynes, Teresa W.
    Murphy, Kyle
    Powiązania:
    https://bibliotekanauki.pl/articles/31343383.pdf
    Data publikacji:
    2019-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph pebbling
    graph rubbling
    optimal rubbling
    t -restricted optimal pebbling
    Opis:
    Let G be a graph with vertex set V and a distribution of pebbles on the vertices of V. A pebbling move consists of removing two pebbles from a vertex and placing one pebble on a neighboring vertex, and a rubbling move consists of removing a pebble from each of two neighbors of a vertex v and placing a pebble on v. We seek an initial placement of a minimum total number of pebbles on the vertices in V, so that no vertex receives more than one pebble and for any given vertex v ∈ V, it is possible, by a sequence of pebbling and rubbling moves, to move at least one pebble to v. This minimum number of pebbles is the 1-restricted optimal rubbling number. We determine the 1-restricted optimal rubbling numbers for Cartesian products. We also present bounds on the 1-restricted optimal rubbling number.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 2; 575-588
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Note on Non-Dominating Set Partitions in Graphs
    Autorzy:
    Desormeaux, Wyatt J.
    Haynes, Teresa W.
    Henning, Michael A.
    Powiązania:
    https://bibliotekanauki.pl/articles/31340558.pdf
    Data publikacji:
    2016-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    total domination
    non-dominating partition
    nontotal dominating partition
    Opis:
    A set $S$ of vertices of a graph $G$ is a dominating set if every vertex not in $S$ is adjacent to a vertex of $S$ and is a total dominating set if every vertex of $G$ is adjacent to a vertex of $S$. The cardinality of a minimum dominating (total dominating) set of $G$ is called the domination (total domination) number. A set that does not dominate (totally dominate) $G$ is called a non-dominating (non-total dominating) set of $G$. A partition of the vertices of $G$ into non-dominating (non-total dominating) sets is a non-dominating (non-total dominating) set partition. We show that the minimum number of sets in a non-dominating set partition of a graph $G$ equals the total domination number of its complement $ \overline{G} $ and the minimum number of sets in a non-total dominating set partition of $G$ equals the domination number of $ \overline{G} $. This perspective yields new upper bounds on the domination and total domination numbers. We motivate the study of these concepts with a social network application.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 4; 1043-1050
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Restrained Domination in Self-Complementary Graphs
    Autorzy:
    Desormeaux, Wyatt J.
    Haynes, Teresa W.
    Henning, Michael A.
    Powiązania:
    https://bibliotekanauki.pl/articles/32083901.pdf
    Data publikacji:
    2021-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    complement
    restrained domination
    self-complementary graph
    Opis:
    A self-complementary graph is a graph isomorphic to its complement. A set S of vertices in a graph G is a restrained dominating set if every vertex in V(G) \ S is adjacent to a vertex in S and to a vertex in V(G) \ S. The restrained domination number of a graph G is the minimum cardinality of a restrained dominating set of G. In this paper, we study restrained domination in self-complementary graphs. In particular, we characterize the self-complementary graphs having equal domination and restrained domination numbers.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 2; 633-645
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Domination Parameters of a Graph and its Complement
    Autorzy:
    Desormeaux, Wyatt J.
    Haynes, Teresa W.
    Henning, Michael A.
    Powiązania:
    https://bibliotekanauki.pl/articles/31342430.pdf
    Data publikacji:
    2018-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination
    complement
    total domination
    connected domination
    clique domination
    restrained domination
    Opis:
    A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G. Placing constraints on a dominating set yields different domination parameters, including total, connected, restrained, and clique domination numbers. In this paper, we study relationships among domination parameters of a graph and its complement.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 1; 203-215
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Downhill domination in graphs
    Autorzy:
    Haynes, Teresa W.
    Hedetniemi, Stephen T.
    Jamieson, Jessie D.
    Jamieson, William B.
    Powiązania:
    https://bibliotekanauki.pl/articles/30148687.pdf
    Data publikacji:
    2014-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    downhill path
    downhill domination number
    Opis:
    A path $π = (v_1, v_2, . . ., v_{k+1})$ in a graph $G = (V,E)$ is a downhill path if for every $i, 1 ≤ i ≤ k, deg(v_i) ≥ deg(v_{i+1})$, where $deg(v_i)$ denotes the degree of vertex $v_i ∈ V$. The downhill domination number equals the minimum cardinality of a set $S ⊆ V$ having the property that every vertex $v ∈ V$ lies on a downhill path originating from some vertex in $S$. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 3; 603-612
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Rainbow Disconnection in Graphs
    Autorzy:
    Chartrand, Gary
    Devereaux, Stephen
    Haynes, Teresa W.
    Hedetniemi, Stephen T.
    Zhang, Ping
    Powiązania:
    https://bibliotekanauki.pl/articles/31342243.pdf
    Data publikacji:
    2018-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge coloring
    rainbow connection
    rainbow disconnection
    Opis:
    Let G be a nontrivial connected, edge-colored graph. An edge-cut R of G is called a rainbow cut if no two edges in R are colored the same. An edge-coloring of G is a rainbow disconnection coloring if for every two distinct vertices u and v of G, there exists a rainbow cut in G, where u and v belong to different components of G − R. We introduce and study the rainbow disconnection number rd(G) of G, which is defined as the minimum number of colors required of a rainbow disconnection coloring of G. It is shown that the rainbow disconnection number of a nontrivial connected graph G equals the maximum rainbow disconnection number among the blocks of G. It is also shown that for a nontrivial connected graph G of order n, rd(G) = n−1 if and only if G contains at least two vertices of degree n − 1. The rainbow disconnection numbers of all grids Pm □ Pn are determined. Furthermore, it is shown for integers k and n with 1 ≤ k ≤ n − 1 that the minimum size of a connected graph of order n having rainbow disconnection number k is n + k − 2. Other results and a conjecture are also presented.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 4; 1007-1021
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Self-coalition graphs
    Autorzy:
    Haynes, Teresa W.
    Hedetniemi, Jason T.
    Hedetniemi, Stephen T.
    McRae, Alice A.
    Mohan, Raghuveer
    Powiązania:
    https://bibliotekanauki.pl/articles/29519279.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    coalitions in graphs
    coalition partitions
    coalition graphs
    domination
    Opis:
    A coalition in a graph $ G = (V,E) $ consists of two disjoint sets $ V_1 $ and $ V_2 $ of vertices, such that neither $ V_1 $ nor $ V_2 $ is a dominating set, but the union $ V_1 ∪ V_2 $ is a dominating set of $ G $. A coalition partition in a graph $ G $ of order $ n = |V| $ is a vertex partition $ π = {V_1, V_2, . . . , V_k} $ such that every set $ V_i $ either is a dominating set consisting of a single vertex of degree $ n − 1 $, or is not a dominating set but forms a coalition with another set $ V_j $ which is not a dominating set. Associated with every coalition partition $ π $ of a graph $ G $ is a graph called the coalition graph of $ G $ with respect to $ π $, denoted $ CG(G, π) $, the vertices of which correspond one-to-one with the sets $ V_1, V_2, . . . , V_k $ of $ π $ and two vertices are adjacent in $ CG(G, π) $ if and only if their corresponding sets in $ π $ form a coalition. The singleton partition $ π_1 $ of the vertex set of $ G $ is a partition of order $ |V| $, that is, each vertex of $ G $ is in a singleton set of the partition. A graph $ G $ is called a self-coalition graph if $ G $ is isomorphic to its coalition graph $ CG(G, π_1)$, where $π_1$ is the singleton partition of $ G $. In this paper, we characterize self-coalition graphs.
    Źródło:
    Opuscula Mathematica; 2023, 43, 2; 173-183
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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