Cyclic graph: различия между версиями
Glk (обсуждение | вклад) (Новая страница: «'''Cyclic graph''' --- циклический граф. The '''cyclic graph''' <math>C(n,k)</math> have a point set <math>V = \{0,1, \ldots,n-1\}</math> and lines …») |
KEV (обсуждение | вклад) Нет описания правки |
||
| Строка 1: | Строка 1: | ||
'''Cyclic graph''' | '''Cyclic graph''' — ''[[циклический граф]]''. | ||
The '''cyclic graph''' <math>C(n,k)</math> have a point set <math>V = \{0,1, | The '''cyclic graph''' <math>\,C(n,k)</math> have a point set <math>\,V = \{0,1,\ldots,n-1\}</math> and lines <math>\,\{i,i+1\}\pmod{n}</math> and <math>\,\{i,i+k\}\pmod{n}</math> | ||
\ldots,n-1\}</math> and lines <math>\{i,i+1\}\pmod{n}</math> and <math>\{i,i+k\}\pmod{n}</math> | (<math>\,i = 1,\ldots,n</math>), where <math>\,k</math> is an integer with <math>\,2 \leq k \leq n-2</math>. If <math>\,G(n,k)</math> is a ''[[circulant graph]]'', then <math>\,C(n,k) \simeq G(n,S)</math> with <math>\,S = \{1, \ldots,\min\{k,n-k\}\}</math>. The [[graph, undirected graph, nonoriented graph|graph]] <math>\,C(n,k)</math> are point-transitive <math>\,3</math>-regular if <math>\,n = 2k</math>, and <math>\,4</math>-regular otherwise. | ||
(<math>i = 1,\ldots,n</math>), where <math>k</math> is an integer with <math>2 \leq k \leq n-2</math>. | |||
If <math>G(n,k)</math> is a ''circulant graph'', then <math>C(n,k) \simeq G(n,S)</math> with | ==Литература== | ||
<math>S = \{1, \ldots,\min\{k,n-k\}\}</math>. The | |||
point-transitive 3-regular if <math>n = 2k</math>, and 4-regular otherwise. | * Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | ||
Текущая версия от 17:18, 9 ноября 2023
Cyclic graph — циклический граф.
The cyclic graph [math]\displaystyle{ \,C(n,k) }[/math] have a point set [math]\displaystyle{ \,V = \{0,1,\ldots,n-1\} }[/math] and lines [math]\displaystyle{ \,\{i,i+1\}\pmod{n} }[/math] and [math]\displaystyle{ \,\{i,i+k\}\pmod{n} }[/math] ([math]\displaystyle{ \,i = 1,\ldots,n }[/math]), where [math]\displaystyle{ \,k }[/math] is an integer with [math]\displaystyle{ \,2 \leq k \leq n-2 }[/math]. If [math]\displaystyle{ \,G(n,k) }[/math] is a circulant graph, then [math]\displaystyle{ \,C(n,k) \simeq G(n,S) }[/math] with [math]\displaystyle{ \,S = \{1, \ldots,\min\{k,n-k\}\} }[/math]. The graph [math]\displaystyle{ \,C(n,k) }[/math] are point-transitive [math]\displaystyle{ \,3 }[/math]-regular if [math]\displaystyle{ \,n = 2k }[/math], and [math]\displaystyle{ \,4 }[/math]-regular otherwise.
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.