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    Wyświetlanie 1-5 z 5
    Tytuł:
    Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
    Autorzy:
    Dettlaff, M.
    Raczek, J.
    Yero, I. G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255785.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    domination
    paired domination
    independent domination
    edge subdivision
    edge multisubdivision
    corona graph
    Opis:
    Given a graph G = (V, E), the subdivision of an edge e = uv ∈ E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision) numbers are denned similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision) numbers of the generalized corona graphs.
    Źródło:
    Opuscula Mathematica; 2016, 36, 5; 575-588
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An application of the selected graph theory domination concepts to transportation networks modelling
    Autorzy:
    Guze, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/135168.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Morska w Szczecinie. Wydawnictwo AMSz
    Tematy:
    domination
    edge-subdivision
    connected bondage number
    bondage-connected number
    transportation network
    modelling
    Opis:
    One of the possibilities when modelling a transport network is to use a graph with vertices and edges. They represent the nodes and arcs of such a network respectively. There are dozens of parameters or characteristics that we can describe in graphs, including the different types of domination number and the problems related to it. The main aim of this paper has been to show the possibilities of the application of the selected domination-oriented concepts to modelling and improving the transportation and/or logistics networks. Firstly, the basic description of domination in graph theory has been introduced. The edge-subdivision and bondage number notations and their implementations to the transportation network description and modelling were then proposed. Furthermore, the possible usage of distinguishing concepts in an exemplary academic transportation network has been shown. Finally, the conclusions and future directions of the work have been presented.
    Źródło:
    Zeszyty Naukowe Akademii Morskiej w Szczecinie; 2017, 52 (124); 97-102
    1733-8670
    2392-0378
    Pojawia się w:
    Zeszyty Naukowe Akademii Morskiej w Szczecinie
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Color-bounded hypergraphs, V: host graphs and subdivisions
    Autorzy:
    Bujtás, Csilla
    Tuza, Zsolt
    Voloshin, Vitaly
    Powiązania:
    https://bibliotekanauki.pl/articles/743863.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    mixed hypergraph
    color-bounded hypergraph
    vertex coloring
    arboreal hypergraph
    hypertree
    feasible set
    host graph
    edge subdivision
    Opis:
    A color-bounded hypergraph is a hypergraph (set system) with vertex set X and edge set = {E₁,...,Eₘ}, together with integers $s_i$ and $t_i$ satisfying $1 ≤ s_i ≤ t_i ≤ |E_i|$ for each i = 1,...,m. A vertex coloring φ is proper if for every i, the number of colors occurring in edge $E_i$ satisfies $s_i ≤ |φ(E_i)| ≤ t_i$. The hypergraph ℋ is colorable if it admits at least one proper coloring.
    We consider hypergraphs ℋ over a "host graph", that means a graph G on the same vertex set X as ℋ, such that each $E_i$ induces a connected subgraph in G. In the current setting we fix a graph or multigraph G₀, and assume that the host graph G is obtained by some sequence of edge subdivisions, starting from G₀.
    The colorability problem is known to be NP-complete in general, and also when restricted to 3-uniform "mixed hypergraphs", i.e., color-bounded hypergraphs in which $|E_i| = 3$ and $1 ≤ s_i ≤ 2 ≤ t_i ≤ 3$ holds for all i ≤ m. We prove that for every fixed graph G₀ and natural number r, colorability is decidable in polynomial time over the class of r-uniform hypergraphs (and more generally of hypergraphs with $|E_i| ≤ r$ for all 1 ≤ i ≤ m) having a host graph G obtained from G₀ by edge subdivisions. Stronger bounds are derived for hypergraphs for which G₀ is a tree.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2011, 31, 2; 223-238
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Introduction to dominated edge chromatic number of a graph
    Autorzy:
    Piri, Mohammad R.
    Alikhani, Saeid
    Powiązania:
    https://bibliotekanauki.pl/articles/2051020.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dominated edge chromatic number
    subdivision
    operation
    corona
    Opis:
    We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph $G$, is a proper edge coloring of $G$ such that each color class is dominated by at least one edge of $G$. The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by $\chi_{dom}^{\prime}(G)$. We obtain some properties of $\chi_{dom}^{\prime}(G)$ and compute it for specific graphs. Also examine the effects on $\chi_{dom}^{\prime}(G)$ when $G$ is modified by operations on vertex and edge of G. Finally, we consider the k-subdivision of G and study the dominated edge chromatic number of these kind of graphs.
    Źródło:
    Opuscula Mathematica; 2021, 41, 2; 245-257
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Irreducible No-Hole L(2, 1)-Coloring of Edge-Multiplicity-Paths-Replacement Graph
    Autorzy:
    Mandal, Nibedita
    Panigrahi, Pratima
    Powiązania:
    https://bibliotekanauki.pl/articles/31342318.pdf
    Data publikacji:
    2018-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    L (2,1)-coloring
    no-hole coloring
    irreducible coloring
    subdivision graph
    edge-multiplicity-paths-replacement graph
    Opis:
    An L(2, 1)-coloring (or labeling) of a simple connected graph G is a mapping f : V (G) → Z+ ∪ {0} such that |f(u)−f(v)| ≥ 2 for all edges uv of G, and |f(u) − f(v)| ≥ 1 if u and v are at distance two in G. The span of an L(2, 1)-coloring f, denoted by span(f), of G is max{f(v) : v ∈ V (G)}. The span of G, denoted by λ(G), is the minimum span of all possible L(2, 1)-colorings of G. For an L(2, 1)-coloring f of a graph G with span k, an integer l is a hole in f if l ∈ (0, k) and there is no vertex v in G such that f(v) = l. An L(2, 1)-coloring is a no-hole coloring if there is no hole in it, and is an irreducible coloring if color of none of the vertices in the graph can be decreased and yield another L(2, 1)-coloring of the same graph. An irreducible no-hole coloring, in short inh-coloring, of G is an L(2, 1)-coloring of G which is both irreducible and no-hole. For an inh-colorable graph G, the inh-span of G, denoted by λinh(G), is defined as λinh(G) = min{span(f) : f is an inh-coloring of G. Given a function h : E(G) → ℕ − {1}, and a positive integer r ≥ 2, the edge-multiplicity-paths-replacement graph G(rPh) of G is the graph obtained by replacing every edge uv of G with r paths of length h(uv) each. In this paper we show that G(rPh) is inh-colorable except possibly the cases h(e) ≥ 2 with equality for at least one but not for all edges e and (i) Δ(G) = 2, r = 2 or (ii) Δ (G) ≥ 3, 2 ≤ r ≤ 4. We find the exact value of λinh(G(rPh)) in several cases and give upper bounds of the same in the remaining. Moreover, we find the value of λ(G(rPh)) in most of the cases which were left by Lü and Sun in [L(2, 1)-labelings of the edge-multiplicity-paths-replacement of a graph, J. Comb. Optim. 31 (2016) 396–404].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 2; 525-552
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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