- 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