Vertex regular graph

Vertex regular graph --- вершинно-регулярный граф.

Let [math]\displaystyle{ G }[/math] be a subgroup of the full automorphism group of a graph [math]\displaystyle{ X }[/math]. We call [math]\displaystyle{ X }[/math] a [math]\displaystyle{ G }[/math]-vertex regular graph, if the action of [math]\displaystyle{ G }[/math] on [math]\displaystyle{ V(X) }[/math] is regular. When [math]\displaystyle{ G = Aut(X) }[/math], we remove the prefix [math]\displaystyle{ G- }[/math] and call [math]\displaystyle{ X }[/math] vertex regular.