Complete rotation: различия между версиями
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'''Complete rotation''' | '''Complete rotation''' — ''[[полное вращение (орграфа)]].'' | ||
Let <math>G = Cay(\Gamma,S)</math> be a Cayley digraph with <math>|S| = d</math>. (See also | Let <math>\,G = Cay(\Gamma,S)</math> be a [[Cayley graph|Cayley]] [[digraph]] with <math>\,|S| = d</math>. (See also | ||
''Associated Cayley digraph''). | ''[[Associated Cayley digraph]]''). | ||
A '''complete rotation''' of <math>G</math> is a group automorphism <math>\omega</math> of | A '''complete rotation''' of <math>\,G</math> is a group automorphism <math>\,\omega</math> of | ||
<math>\Gamma</math> such that for some ordering <math>s_{0}, s_{1}, \ldots, s_{d-1}</math> | <math>\,\Gamma</math> such that for some ordering <math>\,s_{0}, s_{1}, \ldots, s_{d-1}</math> | ||
of the elements of <math>S</math>, we have <math>\omega(s_{i}) = s_{i+1}</math> for every <math>t | of the elements of <math>\,S</math>, we have <math>\,\omega(s_{i}) = s_{i+1}</math> for every <math>\,t\in Z</math>. | ||
\in Z</math>. | |||
Clearly, a rotation is a graph automorphism. A Cayley digraph with a | Clearly, a rotation is a [[graph, undirected graph, nonoriented graph|graph]] [[automorphism]]. A Cayley digraph with a complete rotation is called a '''[[rotational Cayley digraph]]'''. | ||
complete rotation is called a '''rotational Cayley digraph'''. | |||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 10:48, 24 октября 2018
Complete rotation — полное вращение (орграфа).
Let [math]\displaystyle{ \,G = Cay(\Gamma,S) }[/math] be a Cayley digraph with [math]\displaystyle{ \,|S| = d }[/math]. (See also Associated Cayley digraph).
A complete rotation of [math]\displaystyle{ \,G }[/math] is a group automorphism [math]\displaystyle{ \,\omega }[/math] of [math]\displaystyle{ \,\Gamma }[/math] such that for some ordering [math]\displaystyle{ \,s_{0}, s_{1}, \ldots, s_{d-1} }[/math] of the elements of [math]\displaystyle{ \,S }[/math], we have [math]\displaystyle{ \,\omega(s_{i}) = s_{i+1} }[/math] for every [math]\displaystyle{ \,t\in Z }[/math].
Clearly, a rotation is a graph automorphism. A Cayley digraph with a complete rotation is called a rotational Cayley digraph.
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.