Automorphism: различия между версиями
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'''Automorphism''' | '''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 | ||
<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 16:10, 19 декабря 2011
Automorphism — автоморфизм (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.