How to find G-admissible abelian coverings of a graph?

Abstract

Given a finite connected simple graph $\Gamma$, and a subgroup $G$ of its automorphism group, a general method for finding all finite abelian regular coverings of $\Gamma$ that admit a lift of each element of $G$ is developed. As an application, all connected arc-transitive abelian regular coverings of the Petersen graph are classified up to isomorphism.

arXiv comment24 pages, 1 figure

References in corpus (1)

• Lifting automorphisms along abelian regular coverings of graphs

Cited by in corpus (3)

• Lifting homeomorphisms and finite abelian branched covers of the 2-sphere
• A new approach to the genus spectra of abelian $p$-groups
• Lifting graph automorphisms along solvable regular covers