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    Wyświetlanie 1-8 z 8
    Tytuł:
    Determining Graphs by the Complementary Spectrum
    Autorzy:
    Pinheiro, Lucélia K.
    Souza, Bruna S.
    Trevisan, Vilmar
    Powiązania:
    https://bibliotekanauki.pl/articles/31562123.pdf
    Data publikacji:
    2020-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graphs
    complementary eigenvalues
    graph isomorphism
    Opis:
    The complementary spectrum of a connected graph G is the set of the complementary eigenvalues of the adjacency matrix of G. In this note, we discuss the possibility of representing G using this spectrum. On one hand, we give evidence that this spectrum distinguishes more graphs than other standard graph spectra. On the other hand, we show that it is hard to compute the complementary spectrum. In particular, we see that computing the complementary spectrum is equivalent to finding all connected induced subgraphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 2; 607-620
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cyclic Partitions of Complete and Almost Complete Uniform Hypergraphs
    Autorzy:
    Dilbarjot
    Gosselin, Shonda Dueck
    Powiązania:
    https://bibliotekanauki.pl/articles/32305661.pdf
    Data publikacji:
    2022-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    almost self-complementary hypergraph
    uniform hypergraph
    cyclically t -complementary hypergraph
    ( t,k )-complementing permutation
    Opis:
    We consider cyclic partitions of the complete $k$-uniform hypergraph on a finite set $V$, minus a set of $s$ edges, $ s \ge 0 $. An $s$-almost $t$-complementary $k$-hypergraph is a $k$-uniform hypergraph with vertex set $V$ and edge set $E$ for which there exists a permutation $ \theta \in Sym(V)$ such that the sets $E$, $ E^\theta $, $ E^\{\theta^2} $, . . ., $ E^{\theta^{t−1}} $ partition the set of all $k$-subsets of $V$ minus a set of $s$ edges. Such a permutation $ \theta $ is called an $s$-almost $(t, k)$-complementing permutation. The $s$-almost $t$-complementary $k$-hypergraphs are a natural generalization of the almost self-complementary graphs which were previously studied by Clapham, Kamble et al. and Wojda. We prove the existence of an $s$-almost $ p^\alpha $-complementary $k$-hypergraph of order $n$, where $p$ is prime, \( s= \Pi_{i \ge 0 } \binom{n_i}{k_i} \), and $n_i$ and $k_i$ are the entries in the base-$ p^\alpha $ representations of $n$ and $k$, respectively. This existence result yields a combinatorial argument which generalizes Lucas’ classic 1878 number theory result to prime powers, which was originally proved by Davis and Webb in 1990 by another method. In addition, we prove an alternative statement of the necessary and sufficient conditions for the existence of a $ p^\alpha $-complementary $k$-hypergraph, and the equivalence of these two conditions yield an interesting relationship between the base-$p$ representation and the base-$ p^\alpha $ representation of a positive integer $n$. Finally, we determine a set of necessary and sufficient conditions on $n$ for the existence of a $t$-complementary $k$-uniform hypergraph on $n$ vertices for composite values of $t$, extending previous results due to Wojda, Szymański and Gosselin.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 3; 747-758
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Self-complementary hypergraphs
    Autorzy:
    Wojda, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/743928.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    k-uniform hypergraph
    self-complementary hypergraph
    Opis:
    A k-uniform hypergraph H = (V;E) is called self-complementary if there is a permutation σ:V → V, called self-complementing, such that for every k-subset e of V, e ∈ E if and only if σ(e) ∉ E. In other words, H is isomorphic with $H' = (V; \binom{V}{k} - E)$.
    In the present paper, for every k, (1 ≤ k ≤ n), we give a characterization of self-complementig permutations of k-uniform self-complementary hypergraphs of the order n. This characterization implies the well known results for self-complementing permutations of graphs, given independently in the years 1962-1963 by Sachs and Ringel, and those obtained for 3-uniform hypergraphs by Kocay, for 4-uniform hypergraphs by Szymański, and for general (not uniform) hypergraphs by Zwonek.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2006, 26, 2; 217-224
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Almost Self-Complementary 3-Uniform Hypergraphs
    Autorzy:
    Kamble, Lata N.
    Deshpande, Charusheela M.
    Bam, Bhagyashree Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/31342164.pdf
    Data publikacji:
    2017-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    uniform hypergraph
    self-complementary hypergraph
    almost complete 3-uniform hypergraph
    almost self-complementary hypergraph
    quasi regular hypergraph
    Opis:
    It is known that self-complementary 3-uniform hypergraphs on n vertices exist if and only if n is congruent to 0, 1 or 2 modulo 4. In this paper we define an almost self-complementary 3-uniform hypergraph on n vertices and prove that it exists if and only if n is congruent to 3 modulo 4. The structure of corresponding complementing permutation is also analyzed. Further, we prove that there does not exist a regular almost self-complementary 3-uniform hypergraph on n vertices where n is congruent to 3 modulo 4, and it is proved that there exist a quasi regular almost self-complementary 3-uniform hypergraph on n vertices where n is congruent to 3 modulo 4.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 1; 131-140
    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:
    A note on k-uniform self-complementary hypergraphs of given order
    Autorzy:
    Szymański, Artur
    Wojda, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/743151.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    self-complementing permutation
    self-complementary hypergraph
    k-uniform hypergraph
    binomial coefficients
    Opis:
    We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if $\binom{n}{k}$ is even.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2009, 29, 1; 199-202
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Rainbow Total-Coloring of Complementary Graphs and Erdős-Gallai Type Problem For The Rainbow Total-Connection Number
    Autorzy:
    Sun, Yuefang
    Jin, Zemin
    Tu, Jianhua
    Powiązania:
    https://bibliotekanauki.pl/articles/31342242.pdf
    Data publikacji:
    2018-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Rainbow total-coloring
    rainbow total-connection number
    complementary graph
    Erdős-Gallai type problem
    Opis:
    A total-colored graph $G$ is rainbow total-connected if any two vertices of $G$ are connected by a path whose edges and internal vertices have distinct colors. The rainbow total-connection number, denoted by $ rtc(G) $, of a graph $G$ is the minimum number of colors needed to make $G$ rainbow total-connected. In this paper, we prove that $ rtc(G) $ can be bounded by a constant 7 if the following three cases are excluded: $ diam( \overline{G} ) = 2 $, $ diam( \overline{G} ) = 3 $, $ \overline{G} $ contains exactly two connected components and one of them is a trivial graph. An example is given to show that this bound is best possible. We also study Erdős-Gallai type problem for the rainbow total-connection number, and compute the lower bounds and precise values for the function $ f(n, k) $, where $ f(n, k) $ is the minimum value satisfying the following property: if $ |E(G)| \ge f(n, k) $, then $ rtc(G) \le k $.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 4; 1023-1036
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Existence of Quasi Regular and Bi-Regular Self-Complementary 3-Uniform Hypergraphs
    Autorzy:
    Kamble, Lata N.
    Deshpande, Charusheela M.
    Bam, Bhagyashree Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/31340929.pdf
    Data publikacji:
    2016-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    self-complementary hypergraph
    uniform hypergraph
    regular hypergraph
    quasi regular hypergraph
    bi-regular hypergraph
    Opis:
    A k-uniform hypergraph H = (V; E) is called self-complementary if there is a permutation σ : V → V, called a complementing permutation, such that for every k-subset e of V, e ∈ E if and only if σ(e) ∉ E. In other words, H is isomorphic with H′ = (V ; V(k) − E). In this paper we define a bi-regular hypergraph and prove that there exists a bi-regular self-complementary 3-uniform hypergraph on n vertices if and only if n is congruent to 0 or 2 modulo 4. We also prove that there exists a quasi regular self-complementary 3-uniform hypergraph on n vertices if and only if n is congruent to 0 modulo 4.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 2; 419-426
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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