The planar Cayley graphs are effectively enumerable II. (May 2023)

• Record Type: Journal Article
• Authors: Georgakopoulos, Agelos; Hamann, Matthias
• Is Part Of: European journal of combinatorics. Volume 110(2023)
• Publication Date: 2023-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2022.103668
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We show that a group admits a planar, finitely generated, Cayley graph if and only if it admits a special kind of group presentation we introduce, called a planar presentation. Planar presentations can be recognised algorithmically. As a consequence, we obtain an effective enumeration of the planar Cayley graphs, yielding in particular an affirmative answer to a question of Droms et al. asking whether the planar groups can be effectively enumerated.