Upper bounds of orders of automorphism groups of leafless metric graphs

Abstract

AbstractWe prove a tropical analogue of the theorem of Hurwitz: A leafless metric graph of genus [Formula: see text] has at most 12 automorphisms when g = 2 and [Formula: see text] automorphisms when [Formula: see text]. These inequalities are optimal; for each genus, we give all metric graphs which have the maximum numbers of automorphisms. The proof is written in terms of graph theory.

Keywords

• Tropical curves
• automorphisms of graphs
• Betti numbers of graphs
• tropical analogue of the theorem of Hurwitz
• Primary: 14T20
• Secondary: 05C99