Automorphism: различия между версиями

'''Automorphism''' ---  автоморфизм (ор)графа.

'''1.'''  For an undirected graph, see ''Isomorphic graphs''.

'''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

<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

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>.