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    Wyświetlanie 1-10 z 10
    Tytuł:
    On the 12-Representability of Induced Subgraphs of a Grid Graph
    Autorzy:
    Chen, Joanna N.
    Kitaev, Sergey
    Powiązania:
    https://bibliotekanauki.pl/articles/32361728.pdf
    Data publikacji:
    2022-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph representation
    12-representable graph
    grid graph
    forbidden subgraph
    square grid graph
    line grid graph
    Opis:
    The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53]. This notion generalizes the notions of the much studied permutation graphs and co-interval graphs. It is known that any 12-representable graph is a comparability graph, and also that a tree is 12-representable if and only if it is a double caterpillar. Moreover, Jones et al. initiated the study of 12- representability of induced subgraphs of a grid graph, and asked whether it is possible to characterize such graphs. This question of Jones et al. is meant to be about induced subgraphs of a grid graph that consist of squares, which we call square grid graphs. However, an induced subgraph in a grid graph does not have to contain entire squares, and we call such graphs line grid graphs. In this paper we answer the question of Jones et al. by providing a complete characterization of 12-representable square grid graphs in terms of forbidden induced subgraphs. Moreover, we conjecture such a characterization for the line grid graphs and give a number of results towards solving this challenging conjecture. Our results are a major step in the direction of characterization of all 12-representable graphs since beyond our characterization, we also discuss relations between graph labelings and 12-representability, one of the key open questions in the area.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 2; 383-403
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Minimum congestion spanning trees of grids and discrete toruses
    Autorzy:
    Castejón, Alberto
    Ostrovskii, Mikhail
    Powiązania:
    https://bibliotekanauki.pl/articles/744453.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    minimum congestion spanning tree
    grid graph
    discrete torus
    Opis:
    The paper is devoted to estimates of the spanning tree congestion for grid graphs and discrete toruses of dimensions two and three.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2009, 29, 3; 511-519
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Counting Maximal Distance-Independent Sets in Grid Graphs
    Autorzy:
    Euler, Reinhardt
    Oleksik, Paweł
    Skupień, Zdzisław
    Powiązania:
    https://bibliotekanauki.pl/articles/30146434.pdf
    Data publikacji:
    2013-07-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    independent set
    grid graph
    Fibonacci
    Padovan numbers
    transfer matrix method
    Opis:
    Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any $ \mathcal{l} \in \mathbb{N} $, maximal distance-$ \mathcal{l} $ independent (or simply: maximal $ \mathcal{l} $-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied
    Źródło:
    Discussiones Mathematicae Graph Theory; 2013, 33, 3; 531-557
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Error-Correcting Codes from k -Resolving Sets
    Autorzy:
    Bailey, Robert F.
    Yero, Ismael G.
    Powiązania:
    https://bibliotekanauki.pl/articles/31343451.pdf
    Data publikacji:
    2019-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    error-correcting code
    k -resolving set
    k -metric dimension
    covering design
    uncovering
    grid graph
    Opis:
    We demonstrate a construction of error-correcting codes from graphs by means of k-resolving sets, and present a decoding algorithm which makes use of covering designs. Along the way, we determine the k-metric dimension of grid graphs (i.e., Cartesian products of paths).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 2; 341-355
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weighted Laplacians of grids and their application for inspection of spectral graph clustering methods
    Autorzy:
    Kłopotek, Mieczysław
    Wierzchoń, Sławomir
    Kłopotek, Robert
    Powiązania:
    https://bibliotekanauki.pl/articles/1954572.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Gdańska
    Tematy:
    grid graph
    analytical form of graph Laplacians
    spectral clustering
    graph cuts
    graf siatkowy
    analityczna forma grafu Laplacianie
    grupowanie spektralne
    graf cięcia
    Opis:
    This paper investigates the relationship between various types of spectral clustering methods and their kinship to relaxed versions of graph cut methods. This predominantly analytical study exploits the closed (or nearly closed) form of eigenvalues and eigenvectors of unnormalized (combinatorial), normalized, and random walk Laplacians of multidimensional weighted and unweighted grids. We demonstrate that spectral methods can be compared to (normalized) graph cut clustering only if the cut is performed to minimize the sum of the weight square roots (and not the sum of weights) of the removed edges. We demonstrate also that the spectrogram of the regular grid graph can be derived from the composition of spectrograms of path graphs into which such a graph can be decomposed, only for combinatorial Laplacians. It is impossible to do so both for normalized and random-walk Laplacians. We investigate the in-the-limit behavior of combinatorial and normalized Laplacians demonstrating that the eigenvalues of both Laplacians converge to one another with an increase in the number of nodes while their eigenvectors do not. Lastly, we show that the distribution of eigenvalues is not uniform in the limit, violating a fundamental assumption of the compact spectral clustering method.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2021, 25, 3; 329-353
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Limit Conjecture on the Number of Hamiltonian Cycles on Thin Triangular Grid Cylinder Graphs
    Autorzy:
    Bodroža-Pantić, Olga
    Kwong, Harris
    Doroslovački, Rade
    Pantić, Milan
    Powiązania:
    https://bibliotekanauki.pl/articles/31342332.pdf
    Data publikacji:
    2018-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    contractible Hamiltonian cycles
    generating functions
    thin triangular grid cylinder graph
    Opis:
    We continue our research in the enumeration of Hamiltonian cycles (HCs) on thin cylinder grid graphs Cm × Pn+1 by studying a triangular variant of the problem. There are two types of HCs, distinguished by whether they wrap around the cylinder. Using two characterizations of these HCs, we prove that, for fixed m, the number of HCs of both types satisfy some linear recurrence relations. For small m, computational results reveal that the two numbers are asymptotically the same. We conjecture that this is true for all m ≥ 2.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 2; 405-427
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Oriented Chromatic Number of Cartesian Products and Strong Products of Paths
    Autorzy:
    Dybizbański, Janusz
    Nenca, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/31343580.pdf
    Data publikacji:
    2019-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    oriented coloring
    grid
    Opis:
    An oriented coloring of an oriented graph G is a homomorphism from G to H such that H is without selfloops and arcs in opposite directions. We shall say that H is a coloring graph. In this paper, we focus on oriented col- orings of Cartesian products of two paths, called grids, and strong products of two paths, called strong-grids. We show that there exists a coloring graph with nine vertices that can be used to color every orientation of grids with five columns. We also show that there exists a strong-grid with two columns and its orientation which requires 11 colors for oriented coloring. Moreover, we show that every orientation of every strong-grid with three columns can be colored by 19 colors and that every orientation of every strong-grid with four columns can be colored by 43 colors. The above statements were proved with the help of computer programs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 1; 211-223
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Utilization of graph theory in security analysis of power grid
    Autorzy:
    Válek, Dalibor
    Powiązania:
    https://bibliotekanauki.pl/articles/526987.pdf
    Data publikacji:
    2014
    Wydawca:
    Collegium Civitas
    Tematy:
    Security
    matrix
    power grid
    graph
    Opis:
    This paper describes way how to use graph theory in security analysis. As an environment is used network of power lines and devices which are included here. Power grid is considered as a system of nodes which make together graph (network). On the simple example is applied Fiedler´s theory which is able to select the most important power lines of whole network. Components related to these lines are logicly ordered and considered by author´s modified analysis. This method has been improved and optimalized for risks related with illegal acts. Each power grid component has been connected with possible kind of attack and every of this device was gradually evaluated by five coefficients which takes values from 1 to 10. On the coefficient basis was assessed the level of risk. In the last phase the most risky power grid components have been selected. On the selected devices have been proposed security measures.
    Źródło:
    Securitologia; 2014, 2(20); 87-99
    1898-4509
    Pojawia się w:
    Securitologia
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Coloring of the dth Power of the Face-Centered Cubic Grid
    Autorzy:
    Gastineau, Nicolas
    Togni, Olivier
    Powiązania:
    https://bibliotekanauki.pl/articles/32228468.pdf
    Data publikacji:
    2021-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    face-centered cubic grid
    distance coloring
    dth power of graph
    Opis:
    The face-centered cubic grid is a three dimensional 12-regular infinite grid. This graph represents an optimal way to pack spheres in the three-dimensional space. We give lower and upper bounds on the chromatic number of the dth power of the face-centered cubic grid. In particular, in the case d = 2 we prove that the chromatic number of this grid is 13. We also determine sharper bounds for d = 3 and for subgraphs of the face-centered cubic grid.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1001-1020
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multi-sourced power system restoration strategy based on modified Prim’s algorithm
    Autorzy:
    Łukaszewski, Artur
    Nogal, Łukasz
    Powiązania:
    https://bibliotekanauki.pl/articles/2086893.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    self-healing grid
    micro-grid
    reconfiguration
    greedy algorithms
    graph theory
    simulations
    Prim’s algorithm
    siatka samoleczenia
    mikrosiatka
    rekonfiguracja
    algorytmy zachłanne
    teoria grafów
    symulacje
    algorytm Prima
    Opis:
    Self-healing grids are one of the most developing concepts applied in electrical engineering. Each restoration strategy requires advanced algorithms responsible for the creation of local power systems. Multi-agent automation solutions dedicated for smart grids are mostly based on Prim’s algorithm. Graph theory in that field also leaves many problems unsolved. This paper is focused on a variation of Prim’s algorithm utility for a multi-sourced power system topology. The logic described in the paper is a novel concept combined with a proposal of a multi-parametrized weight calculation formula representing transmission features of energy delivered to loads present in a considered grid. The weight is expressed as the combination of three elements: real power, reactive power, and real power losses. The proposal of a novel algorithm was verified in a simulation model of a power system. The new restoration logic was compared with the proposal of the strategy presented in other recently published articles. The novel concept of restoration strategy dedicated to multi-sourced power systems was verified positively by simulations. The proposed solution proved its usefulness and applicability.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 5; e137942, 1--12
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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