Complete rotation: различия между версиями

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'''Complete rotation''' --- полное вращение [орграфа].  
'''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 rotationполное 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.