Temat: generalized Petersen graph - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Hamilton Cycles in Double Generalized Petersen Graphs
Autorzy:: Sakamoto, Yutaro
Powiązania:: https://bibliotekanauki.pl/articles/31343695.pdf
Data publikacji:: 2019-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: double generalized Petersen graph
Hamilton cycle
Opis:: Coxeter referred to generalizing the Petersen graph. Zhou and Feng modified the graphs and introduced the double generalized Petersen graphs (DGPGs). Kutnar and Petecki proved that DGPGs are Hamiltonian in special cases and conjectured that all DGPGs are Hamiltonian. In this paper, we prove the conjecture by constructing Hamilton cycles in any given DGPG.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 1; 117-123
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: α-Labelings of a Class of Generalized Petersen Graphs
Autorzy:: Benini, Anna
Pasotti, Anita
Powiązania:: https://bibliotekanauki.pl/articles/31339104.pdf
Data publikacji:: 2015-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: generalized Petersen graph
α-labeling
graph decomposition
Opis:: An α-labeling of a bipartite graph $Γ$ of size $e$ is an injective function $f : V (Γ) → {0, 1, 2, . . ., e}$ such that ${|ƒ(x) − ƒ(y)| : [x, y] ∈ E(Γ)} = {1, 2, . . ., e}$ and with the property that its maximum value on one of the two bipartite sets does not reach its minimum on the other one. We prove that the generalized Petersen graph $P_{Sn,3}$ admits an α-labeling for any integer $n ≥ 1$ confirming that the conjecture posed by Vietri in [10] is true. In such a way we obtain an infinite class of decompositions of complete graphs into copies of $P_{Sn,3}$.
Źródło:: Discussiones Mathematicae Graph Theory; 2015, 35, 1; 43-53
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: The Crossing Number of Join of the Generalized Petersen Graph P (3, 1) with Path and Cycle
Autorzy:: Ouyang, Zhang Dong
Wang, Jing
Huang, Yuan Qiu
Powiązania:: https://bibliotekanauki.pl/articles/31342419.pdf
Data publikacji:: 2018-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: crossing number
drawing
join product
generalized Petersen graph
Opis:: There are only few results concerning the crossing numbers of join of some graphs. In this paper, the crossing numbers of join products for the generalized Petersen graph P(3, 1) with n isolated vertices as well as with the path P_n on n vertices and with the cycle C_n are determined.
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 2; 351-370
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: On the Star Chromatic Index of Generalized Petersen Graphs
Autorzy:: Zhu, Enqiang
Shao, Zehui
Powiązania:: https://bibliotekanauki.pl/articles/32083878.pdf
Data publikacji:: 2021-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: star edge-coloring
star chromatic index
generalized Petersen graph
Opis:: The star $k$-edge-coloring of graph $G$ is a proper edge coloring using $k$ colors such that no path or cycle of length four is bichromatic. The minimum number $k$ for which $G$ admits a star $k$-edge-coloring is called the star chromatic index of $G$, denoted by $χ_s^′(G)$. Let $GCD(n, k)$ be the greatest common divisor of $n$ and $k$. In this paper, we give a necessary and sufficient condition of $χ_s^′(P(n, k)) = 4$ for a generalized Petersen graph $P(n, k)$ and show that “almost all” generalized Petersen graphs have a star 5-edge-colorings. Furthermore, for any two integers $k$ and $n(≥2k + 1)$ such that $GCD(n, k) ≥ 3, P (n, k)$ has a star 5-edge-coloring, with the exception of the case that $GCD(n, k) = 3$, $k ≠ GCD(n, k)$ and $\frac{n}{3}≡1(mod3)$.
Źródło:: Discussiones Mathematicae Graph Theory; 2021, 41, 2; 427-439
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Power Domination in the Generalized Petersen Graphs
Autorzy:: Zhao, Min
Shan, Erfang
Kang, Liying
Powiązania:: https://bibliotekanauki.pl/articles/31348324.pdf
Data publikacji:: 2020-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: power domination
domination
generalized Petersen graph
electric power system
Opis:: The problem of monitoring an electric power system by placing as few measurement devices in the system can be formulated as a power dominating set problem in graph theory. The power domination number of a graph is the minimum cardinality of a power dominating set. Xu and Kang [On the power domination number of the generalized Petersen graphs, J. Comb. Optim. 22 (2011) 282–291] study the exact power domination number for the generalized Petersen graph P (3k, k), and propose the following problem: determine the power domination number for the generalized Petersen graph P (4k, k) or P (ck, k). In this paper we give the power domination number for P (4k, k) and present a sharp upper bound on the power domination number for the generalized Petersen graph P (ck, k).
Źródło:: Discussiones Mathematicae Graph Theory; 2020, 40, 3; 695-712
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

Tytuł:: Lower Bound on the Number of Hamiltonian Cycles of Generalized Petersen Graphs
Autorzy:: Lu, Weihua
Yang, Chao
Ren, Han
Powiązania:: https://bibliotekanauki.pl/articles/32083755.pdf
Data publikacji:: 2020-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: generalized Petersen graph
Hamiltonian cycle
partition number
1-factor
Opis:: In this paper, we investigate the number of Hamiltonian cycles of a generalized Petersen graph $ P(N, k) $ and prove that $ \Psi(P(N,3)) \ge N \cdot \alpha_N $, where $ \Psi (P(N, 3)) $ is the number of Hamiltonian cycles of $P(N, 3)$ and $ \alpha_N $ satisfies that for any $ \epsilon > 0 $, there exists a positive integer $M$ such that when $ N > M $, $ ((1− \epsilon ) \frac{ (1−r^3) }{6r^3+5r^2+3) }( 1/r )^{N+2} < \alpha_N < ( (1+ɛ) \frac{ (1−r^3) }{6r^3+5r^2+3) }( 1/r )^{N+2} $, where $ 1/r = \text{max} \{ | \frac{1}{r_j} | : j=1,2,…,6 \} $, and each $ r_j $ is a root of equation $ x^6 + x^5 + x^3 − 1 = 0 $, $ r \approx 0.782 $. This shows that $ \Psi (P (N, 3) $ is exponential in $N$ and also deduces that the number of 1-factors of $ P(N, 3)$ is exponential in $N$.
Źródło:: Discussiones Mathematicae Graph Theory; 2020, 40, 1; 297-305
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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