Temat: permutation graph - 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:: 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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