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    Wyświetlanie 1-5 z 5
    Tytuł:
    On the crossing numbers of join products of five graphs of order six with the discrete graph
    Autorzy:
    Stas, Michal
    Powiązania:
    https://bibliotekanauki.pl/articles/952808.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    graph
    drawing
    crossing number
    join product
    cyclic permutation
    Opis:
    The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product G* + Dn, where the disconnected graph G* of order six consists of one isolated vertex and of one edge joining two nonadjacent vertices of the 5-cycle. In our proof, the idea of cyclic permutations and their combinatorial properties will be used. Finally, by adding new edges to the graph G*, the crossing numbers of Gi + Dn for four other graphs Gi of order six will be also established
    Źródło:
    Opuscula Mathematica; 2020, 40, 3; 383-397
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the crossing numbers of join products of $W_4 + P_n$ and $W_4 + C_n$
    Autorzy:
    Stas, Michal
    Valiska, Juraj
    Powiązania:
    https://bibliotekanauki.pl/articles/1397319.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    graph
    crossing number
    join product
    cyclic permutation
    path
    cycle
    Opis:
    The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of the paper is to give the crossing number of the join product $W_4 + P_n$ and $W_4 + C_n$ for the wheel $W_4$ on five vertices, where $P_n$ and $C_n$ are the path and the cycle on n vertices, respectively. Yue et al. conjectured that the crossing number of $W_m + C_n$ is equal to $Z(m+1)Z(n)+(Z(m)-1)[n/2]+n+[m/2]+2$, for all m,n ≥ 3, and where the Zarankiewicz’s number $Z(n)=[n/2][{n-1}/2]$ is defined for n ≥ 1. Recently, this conjecture was proved for $W_3 + C_n$ by Klesc. We establish the validity of this conjecture for $W_4 + C_n$ and we also offer a new conjecture for the crossing number of the join product $W_m + P_n$ for m ≥ 3 and n ≥ 2.
    Źródło:
    Opuscula Mathematica; 2021, 41, 1; 95-112
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The crossing numbers of join products of four graphs of order five with paths and cycles
    Autorzy:
    Staš, Michal
    Timková, Mária
    Powiązania:
    https://bibliotekanauki.pl/articles/29519472.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    graph
    crossing number
    join product
    path
    cycle
    separating cycle
    Opis:
    The crossing number $ \text{cr} (G) $ of a graph $ G $ is the minimum number of edge crossings over all drawings of $ G $ in the plane. In the paper, we extend known results concerning crossing numbers of join products of four small graphs with paths and cycles. The crossing numbers of the join products $ G^∗ + P_n $ and $ G^∗ + C_n $ for the disconnected graph $ G^∗ $ consisting of the complete tripartite graph $ K_{1,1,2} $ and one isolated vertex are given, where $ P_n $ and $ C_n $ are the path and the cycle on $ n $ vertices, respectively. In the paper also the crossing numbers of $ H^∗ + P_n $ and $ H^∗ + C_n $ are determined, where $ H^∗ $ is isomorphic to the complete tripartite graph $ K_{1,1,3} $. Finally, by adding new edges to the graphs $ G^∗ $ and $ H^∗ $, we are able to obtain crossing numbers of join products of two other graphs $ G_1 $ and $ H_1 $ with paths and cycles.
    Źródło:
    Opuscula Mathematica; 2023, 43, 6; 865-883
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The crossing numbers of join products of paths with three graphs of order five
    Autorzy:
    Staš, Michal
    Švecová, Mária
    Powiązania:
    https://bibliotekanauki.pl/articles/2216156.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    graph
    crossing number
    join product
    cyclic permutation
    path
    Opis:
    The main aim of this paper is to give the crossing number of the join product $G^∗ + P_n$ for the disconnected graph $G^$∗ of order five consisting of the complete graph $K_4$ and one isolated vertex, where $P_n$ is the path on n vertices. The proofs are done with the help of a lot of well-known exact values for the crossing numbers of the join products of subgraphs of the graph $G^∗$ with the paths. Finally, by adding new edges to the graph $G^∗$, we are able to obtain the crossing numbers of the join products of two other graphs with the path $P_n$.
    Źródło:
    Opuscula Mathematica; 2022, 42, 4; 635-651
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cyclic Permutations in Determining Crossing Numbers
    Autorzy:
    Klešč, Marián
    Staš, Michal
    Powiązania:
    https://bibliotekanauki.pl/articles/32222545.pdf
    Data publikacji:
    2022-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    drawing
    crossing number
    join product
    cyclic permutation
    Opis:
    The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied. In the paper, we extend know results concerning crossing numbers of join products of small graphs with discrete graphs. The crossing number of the join product G*+ Dn for the disconnected graph G* consisting of five vertices and of three edges incident with the same vertex is given. Up to now, the crossing numbers of G + Dn were done only for connected graphs G. In the paper also the crossing numbers of G*+ Pn and G* + Cn are given. The paper concludes by giving the crossing numbers of the graphs H + Dn, H + Pn, and H + Cn for four different graphs H with |E(H)| ≤ |V (H)|. The methods used in the paper are new. They are based on combinatorial properties of cyclic permutations.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1163-1183
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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