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    Wyświetlanie 1-15 z 15
    Tytuł:
    Trees with Distinguishing Index Equal Distinguishing Number Plus One
    Autorzy:
    Alikhani, Saeid
    Klavžar, Sandi
    Lehner, Florian
    Soltani, Samaneh
    Powiązania:
    https://bibliotekanauki.pl/articles/31804165.pdf
    Data publikacji:
    2020-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    automorphism group
    distinguishing index
    distinguishing number
    tree
    unicyclic graph
    Opis:
    The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism. It is known that for every graph G we have D′ (G) ≤ D(G) + 1. In this note we characterize finite trees for which this inequality is sharp. We also show that if G is a connected unicyclic graph, then D′ (G) = D(G).
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 3; 875-884
    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
    Tytuł:
    Total connected domination game
    Autorzy:
    Bujtás, Csilla
    Henning, Michael A.
    Iršič, Vesna
    Klavžar, Sandi
    Powiązania:
    https://bibliotekanauki.pl/articles/2050904.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    connected domination game
    total connected domination game
    graph product
    tree
    Opis:
    The (total) connected domination game on a graph $G$ is played by two players, Dominator and Staller, according to the standard (total) domination game with the additional requirement that at each stage of the game the selected vertices induce a connected subgraph of $G$. If Dominator starts the game and both players play optimally, then the number of vertices selected during the game is the (total) connected game domination number $(\gamma_{tcg}(G))(\gamma_{cg(G)})$ of $G$. We show that $\gamma_{tcg}(G) \in \{\gamma_{cg}(G), \gamma_{cg}(G)+1, \gamma_{cg}(G)+2\}$, and consequently define $G$ as Class $i$ if $\gamma_{tcg}(G) = \gamma_{cg}(G)+i$ for $i \in \{0, 1, 2\}$. A large family of Class 0 graphs is constructed which contains all connected Cartesian product graphs and connected direct product graphs with minimum degree at least 2. We show that no tree is Class 2 and characterize Class 1 trees. We provide an infinite family of Class 2 bipartite graphs.
    Źródło:
    Opuscula Mathematica; 2021, 41, 4; 453-464
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The General Position Problem on Kneser Graphs and on Some Graph Operations
    Autorzy:
    Ghorbani, Modjtaba
    Maimani, Hamid Reza
    Momeni, Mostafa
    Mahid, Farhad Rahimi
    Klavžar, Sandi
    Rus, Gregor
    Powiązania:
    https://bibliotekanauki.pl/articles/32222714.pdf
    Data publikacji:
    2021-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    general position set
    Kneser graphs
    Cartesian product of graphs
    corona over graphs
    line graphs
    Opis:
    A vertex subset S of a graph G is a general position set of G if no vertex of S lies on a geodesic between two other vertices of S. The cardinality of a largest general position set of G is the general position number (gp-number) gp(G) of G. The gp-number is determined for some families of Kneser graphs, in particular for K(n, 2), n ≥ 4, and K(n, 3), n ≥ 9. A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1199-1213
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong Geodetic Problem in Networks
    Autorzy:
    Manuel, Paul
    Klavžar, Sandi
    Xavier, Antony
    Arokiaraj, Andrew
    Thomas, Elizabeth
    Powiązania:
    https://bibliotekanauki.pl/articles/32083731.pdf
    Data publikacji:
    2020-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    geodetic problem
    strong geodetic problem
    Apollonian networks
    Sierpiński graphs
    computational complexity
    Opis:
    In order to model certain social network problems, the strong geodetic problem and its related invariant, the strong geodetic number, are introduced. The problem is conceptually similar to the classical geodetic problem but seems intrinsically more difficult. The strong geodetic number is compared with the geodetic number and with the isometric path number. It is determined for several families of graphs including Apollonian networks. Applying Sierpiński graphs, an algorithm is developed that returns a minimum path cover of Apollonian networks corresponding to the strong geodetic number. It is also proved that the strong geodetic problem is NP-complete.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 1; 307-321
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some results on total domination in direct products of graphs
    Autorzy:
    Dorbec, Paul
    Gravier, Sylvain
    Klavžar, Sandi
    Spacapan, Simon
    Powiązania:
    https://bibliotekanauki.pl/articles/743885.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    direct product
    total domination
    k-tuple domination
    open packing
    domination
    Opis:
    Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2006, 26, 1; 103-112
    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:
    On the rainbow connection of Cartesian products and their subgraphs
    Autorzy:
    Klavžar, Sandi
    Mekiš, Gašper
    Powiązania:
    https://bibliotekanauki.pl/articles/743307.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    rainbow connection
    strong rainbow connection
    Cartesian product of graphs
    isometric subgraph
    hypercube
    Opis:
    Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and non-existence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above by the rainbow connection number of the hypercube. Isometric subgraphs of hypercubes with the rainbow connection number as small as possible compared to the rainbow connection of the hypercube are constructed. The concept of c-strong rainbow connected coloring is introduced. In particular, it is proved that the so-called Θ-coloring of an isometric subgraph of a hypercube is its unique optimal c-strong rainbow connected coloring.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 4; 783-793
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Grundy Total Domination Number in Product Graphs
    Autorzy:
    Brešar, Boštjan
    Bujtás, Csilla
    Gologranc, Tanja
    Klavžar, Sandi
    Košmrlj, Gašper
    Marc, Tilen
    Patkós, Balázs
    Tuza, Zsolt
    Vizer, Máté
    Powiązania:
    https://bibliotekanauki.pl/articles/32083828.pdf
    Data publikacji:
    2021-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    total domination
    Grundy total domination number
    graph product
    Opis:
    A longest sequence $(v_1, . . ., v_k)$ of vertices of a graph $G$ is a Grundy total dominating sequence of $G$ if for all $i$, \(N(υ_i)\backslash\bigcup_{j=1}^{i-1}N(υ_j)≠∅\). The length $k$ of the sequence is called the Grundy total domination number of $G$ and denoted $\gamma_{gr}^t(G)$. In this paper, the Grundy total domination number is studied on four standard graph products. For the direct product we show that $\gamma_{gr}^t(G×H)≥\gamma_{gr}^t(G)\gamma_{gr}^t(H)$, conjecture that the equality always holds, and prove the conjecture in several special cases. For the lexicographic product we express $\gamma_{gr}^t(G∘H)$ in terms of related invariant of the factors and find some explicit formulas for it. For the strong product, lower bounds on $\gamma_{gr}^t(G⊠H)$ are proved as well as upper bounds for products of paths and cycles. For the Cartesian product we prove lower and upper bounds on the Grundy total domination number when factors are paths or cycles.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 1; 225-247
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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:
    Isomorphic components of Kronecker product of bipartite graphs
    Autorzy:
    Jha, Pranava
    Klavžar, Sandi
    Zmazek, Blaž
    Powiązania:
    https://bibliotekanauki.pl/articles/971945.pdf
    Data publikacji:
    1997
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Kronecker product
    bipartite graphs
    graph isomorphism
    Opis:
    Weichsel (Proc. Amer. Math. Soc. 13 (1962) 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the above condition and it is conjectured that the converse is true in general.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1997, 17, 2; 301-309
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    How Long Can One Bluff in the Domination Game?
    Autorzy:
    Brešar, Boštan
    Dorbec, Paul
    Klavžar, Sandi
    Košmrlj, Gašpar
    Powiązania:
    https://bibliotekanauki.pl/articles/31341979.pdf
    Data publikacji:
    2017-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination game
    game domination number
    bluff graphs
    minus graphs
    generalized Petersen graphs
    Kneser graphs
    Cartesian product of graphs
    Hamming graphs
    Opis:
    The domination game is played on an arbitrary graph G by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. minus graphs with game domination number equal to 3 are characterized. Double bluff graphs are also introduced and it is proved that Kneser graphs K(n, 2), n ≥ 6, are double bluff. The domination game is also studied on generalized Petersen graphs and on Hamming graphs. Several generalized Petersen graphs that are bluff graphs but not vertex-transitive are found. It is proved that Hamming graphs are not double bluff.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 2; 337-352
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Edge-Transitive Lexicographic and Cartesian Products
    Autorzy:
    Imrich, Wilfried
    Iranmanesh, Ali
    Klavžar, Sandi
    Soltani, Abolghasem
    Powiązania:
    https://bibliotekanauki.pl/articles/31340755.pdf
    Data publikacji:
    2016-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    edge-transitive graph
    vertex-transitive graph
    lexicographic product of graphs
    Cartesian product of graphs
    Opis:
    In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦ H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ∘ H is non-trivial and complete, then G ∘ H is edge-transitive if and only if H is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao [11]. For the Cartesian product it is shown that every connected Cartesian product of at least two non-trivial factors is edge-transitive if and only if it is the Cartesian power of a connected, edge- and vertex-transitive graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 4; 857-865
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Domination Game Critical Graphs
    Autorzy:
    Bujtás, Csilla
    Klavžar, Sandi
    Košmrlj, Gašper
    Powiązania:
    https://bibliotekanauki.pl/articles/31234048.pdf
    Data publikacji:
    2015-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination number
    domination game
    domination game critical graphs
    powers of cycles
    trees
    Opis:
    The domination game is played on a graph $G$ by two players who alternately take turns by choosing a vertex such that in each turn at least one previously undominated vertex is dominated. The game is over when each vertex becomes dominated. One of the players, namely Dominator, wants to finish the game as soon as possible, while the other one wants to delay the end. The number of turns when Dominator starts the game on $G$ and both players play optimally is the graph invariant $ \gamma_g (G) $, named the game domination number. Here we study the $ \gamma_g$-critical graphs which are critical with respect to vertex predomination. Besides proving some general properties, we characterize $ \gamma_g$-critical graphs with $ \gamma_g = 2$ and with $ \gamma_g = 3$, moreover for each n we identify the (infinite) class of all $\gamma_g$-critical ones among the $n$th powers $ C_N^n$ of cycles. Along the way we determine $\gamma_{g} ( C_N^n ) $ for all $n$ and $N$. Results of a computer search for $ \gamma_g$-critical trees are presented and several problems and research directions are also listed.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2015, 35, 4; 781-796
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Survey on Packing Colorings
    Autorzy:
    Brešar, Boštjan
    Ferme, Jasmina
    Klavžar, Sandi
    Rall, Douglas F.
    Powiązania:
    https://bibliotekanauki.pl/articles/31804166.pdf
    Data publikacji:
    2020-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    packing coloring
    packing chromatic number
    subcubic graph
    S -packing chromatic number
    computational complexity
    Opis:
    If S = (a1, a2, . . .) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1, X2, . . . such that for each pair of distinct vertices in the set Xi, the distance between them is larger than ai. If there exists an integer k such that V (G) = X1 ∪ ∪ Xk, then the partition is called an S-packing k-coloring. The S-packing chromatic number of G is the smallest k such that G admits an S-packing k-coloring. If ai = i for every i, then the terminology reduces to packing colorings and packing chromatic number. Since the introduction of these generalizations of the chromatic number in 2008 more than fifty papers followed. Here we survey the state of the art on the packing coloring, and its generalization, the S-packing coloring. We also list several conjectures and open problems.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 4; 923-970
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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