Regular graph coverings whose covering transformation groups have the isomorphism extension property
The authors obtain several new algebraic characterizations for isomorphic regular graph coverings and enumerate isomorphism classes of \(A\)-coverings of a graph \(G\) with respect to any group of automorphisms of \(G\) which fix a spanning tree, when the covering transformation group \(A\) has the isomorphism extension property (every isomorphism between any two isomorphic subgroups of \(A\) can be extended to an automorphism of \(A\)). In particular, for \(A\) cyclic, dihedral, or \(\mathbb{Z}_p\oplus \mathbb{Z}_p\), they obtain complete numerical enumerations of the isomorphism classes of \(A\)-coverings with respect to the trivial automorphism group of \(G\). The results are applied to bouquets of circles.
scientific article; zbMATH DE number 858078