2019/01/02 by Agelos Georgakopoulos, Georgakopoulos, Agelos, Matthias Hamann +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #05C10 (secondary) #05C25 #20F05 (primary) #Advanced Graph Theory Research #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1901.00347
openalex publication_date 2019/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.