Automorphism: различия между версиями

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'''Automorphism''' ---  автоморфизм (ор)графа.
'''Automorphism''' — ''[[автоморфизм графа|автоморфизм (ор)графа]].''


'''1.'''  For an undirected graph, see ''Isomorphic graphs''.
'''1.'''  For an [[graph, undirected graph, nonoriented graph|undirected graph]], see ''[[Isomorphic graphs]]''.


'''2.''' For a directed graph,  '''automorphism''' is a permutation <math>\alpha</math> of <math>V(G)</math>
'''2.''' For a [[directed graph]],  '''automorphism''' is a permutation <math>\,\alpha</math> of <math>\,V(G)</math>
such  that  the  number  of <math>(x,y)</math>-edges is the same as the number of
such  that  the  number  of <math>\,(x,y)</math>-[[edge|edges]] is the same as the number of
<math>(\alpha(x),  \alpha(y))</math>-edges <math>(x,y \in V(G))</math>. We also speak of the
<math>(\,\alpha(x),  \alpha(y))</math>-edges <math>(x,y \in V(G))</math>. We also speak of the
''' automorphism''' of a graph <math>G</math> with colored edges.  This means a permutation
'''automorphism''' of a graph <math>\,G</math> with colored edges.  This means a permutation
<math>\alpha</math> such that the number of <math>(x,y)</math>-edges is the same as the
<math>\,\alpha</math> such that the number of <math>\,(x,y)</math>-edges is the same as the
number of <math>(\alpha(x), \alpha(y))</math>-edges with any given color.
number of <math>(\,\alpha(x), \alpha(y))</math>-edges with any given color.


The set of all automorphisms of a (di)graph forms a permutation group <math>A(G)</math>.
The set of all automorphisms of a (di)graph forms a permutation group <math>\,A(G)</math>.
 
==Литература==
 
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.

Текущая версия от 16:30, 23 октября 2018

Automorphismавтоморфизм (ор)графа.

1. For an undirected graph, see Isomorphic graphs.

2. For a directed graph, automorphism is a permutation [math]\displaystyle{ \,\alpha }[/math] of [math]\displaystyle{ \,V(G) }[/math] such that the number of [math]\displaystyle{ \,(x,y) }[/math]-edges is the same as the number of [math]\displaystyle{ (\,\alpha(x), \alpha(y)) }[/math]-edges [math]\displaystyle{ (x,y \in V(G)) }[/math]. We also speak of the automorphism of a graph [math]\displaystyle{ \,G }[/math] with colored edges. This means a permutation [math]\displaystyle{ \,\alpha }[/math] such that the number of [math]\displaystyle{ \,(x,y) }[/math]-edges is the same as the number of [math]\displaystyle{ (\,\alpha(x), \alpha(y)) }[/math]-edges with any given color.

The set of all automorphisms of a (di)graph forms a permutation group [math]\displaystyle{ \,A(G) }[/math].

Литература

  • Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.