Jordan-like characterization of automorphism groups of planar graphs

TL;DR

This paper provides a complete recursive characterization of all automorphism groups of planar graphs using inhomogeneous wreath products, improving upon Babai's earlier description by integrating combinatorics, group theory, and geometry.

Contribution

It introduces a new recursive framework for describing automorphism groups of planar graphs, extending Babai's 1975 characterization with a more comprehensive approach.

Findings

Complete recursive description of automorphism groups of planar graphs

Characterization formulated via inhomogeneous wreath products

Enhanced understanding of group structures in planar graph automorphisms

Abstract

We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of inhomogeneous wreath products. In the proof, we combine techniques from combinatorics, group theory, and geometry. This significantly improves the Babai's description (1975).