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    Wyświetlanie 1-6 z 6
    Tytuł:
    Median and quasi-median direct products of graphs
    Autorzy:
    Brešar, Boštjan
    Jha, Pranava
    Klavžar, Sandi
    Zmazek, Blaž
    Powiązania:
    https://bibliotekanauki.pl/articles/744332.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    median graph
    direct product
    quasi-median graph
    isometric embeddings
    convexity
    Opis:
    Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P₃ is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K₂ are proved, and it is shown that the only nonbipartite quasi-median direct product is K₃×K₃.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 183-196
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modular and median signpost systems and their underlying graphs
    Autorzy:
    Mulder, Henry
    Nebeský, Ladislav
    Powiązania:
    https://bibliotekanauki.pl/articles/743171.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    signpost system
    modular graph
    median graph
    Opis:
    The concept of a signpost system on a set is introduced. It is a ternary relation on the set satisfying three fairly natural axioms. Its underlying graph is introduced. When the underlying graph is disconnected some unexpected things may happen. The main focus are signpost systems satisfying some extra axioms. Their underlying graphs have lots of structure: the components are modular graphs or median graphs. Yet another axiom guarantees that the underlying graph is also connected. The main results of this paper concern if-and-only-if characterizations involving signpost systems satisfying additional axioms on the one hand and modular, respectively median graphs on the other hand.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2003, 23, 2; 309-324
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Arboreal structure and regular graphs of median-like classes
    Autorzy:
    Brešar, Bostjan
    Powiązania:
    https://bibliotekanauki.pl/articles/743403.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    median graph
    tree
    gatedness
    amalgam
    periphery
    regular graph
    Opis:
    We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime graph minus a vertex. Therefore, these graphs admit a peripheral elimination procedure which is a generalization of analogous procedure in median graphs. We characterize regular graphs of these classes whenever they enjoy an additional property. As a corollary we derive that regular weakly median graphs are precisely Cartesian products in which each factor is a complete graph or a hyperoctahedron.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2003, 23, 2; 215-225
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The periphery graph of a median graph
    Autorzy:
    Brešar, Boštjan
    Changat, Manoj
    Subhamathi, Ajitha
    Tepeh, Aleksandra
    Powiązania:
    https://bibliotekanauki.pl/articles/744496.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    median graph
    Cartesian product
    geodesic
    periphery
    peripheral expansion
    Opis:
    The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are path-like median graphs with arbitrarily large geodetic number. Peripheral expansion with respect to periphery graph is also considered, and connections with the concept of crossing graph are established.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2010, 30, 1; 17-32
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On θ-graphs of partial cubes
    Autorzy:
    Klavžar, Sandi
    Kovse, Matjaz
    Powiązania:
    https://bibliotekanauki.pl/articles/743784.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    intersection graph
    partial cube
    median graph
    expansion theorem
    Cartesian product of graphs
    Opis:
    The Θ-graph Θ(G) of a partial cube G is the intersection graph of the equivalence classes of the Djoković-Winkler relation. Θ-graphs that are 2-connected, trees, or complete graphs are characterized. In particular, Θ(G) is complete if and only if G can be obtained from K₁ by a sequence of (newly introduced) dense expansions. Θ-graphs are also compared with familiar concepts of crossing graphs and τ-graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2007, 27, 2; 313-321
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Tree-like isometric subgraphs of hypercubes
    Autorzy:
    Brešar, Bostjan
    Imrich, Wilfried
    Klavžar, Sandi
    Powiązania:
    https://bibliotekanauki.pl/articles/743405.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    isometric embeddings
    partial cubes
    expansion procedures
    trees
    median graphs
    graph automorphisms
    automorphism groups
    dismantlable graphs
    Opis:
    Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a generalization of median graphs. Just as median graphs they capture numerous properties of trees, but may contain larger classes of graphs that may be easier to recognize than the class of median graphs. We investigate the structure of tree-like partial cubes, characterize them, and provide examples of similarities with trees and median graphs. For instance, we show that the cube graph of a tree-like partial cube is dismantlable. This in particular implies that every tree-like partial cube G contains a cube that is invariant under every automorphism of G. We also show that weak retractions preserve tree-like partial cubes, which in turn implies that every contraction of a tree-like partial cube fixes a cube. The paper ends with several Frucht-type results and a list of open problems.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2003, 23, 2; 227-240
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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