Temat: join - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

Skocz do pozycji: 2.

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

Skocz do pozycji: 3.

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*+ D_n 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 + D_n were done only for connected graphs G. In the paper also the crossing numbers of G*+ P_n and G* + C_n are given. The paper concludes by giving the crossing numbers of the graphs H + D_n, H + P_n, and H + C_n 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

Skocz do pozycji: 4.

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

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