Edge regular graph

Edge regular graph --- реберно-регулярный граф.

Let [math]\displaystyle{ X }[/math] be a graph and [math]\displaystyle{ A = Aut(X) }[/math] be the full automorphism group of [math]\displaystyle{ X }[/math]. Let [math]\displaystyle{ G }[/math] be a subgroup of the full automorphism group [math]\displaystyle{ A }[/math] of the graph [math]\displaystyle{ X }[/math]. We call [math]\displaystyle{ X }[/math] [math]\displaystyle{ G }[/math]-edge regular if the action of [math]\displaystyle{ G }[/math] on [math]\displaystyle{ E(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] edge regular.