We study semigroups of labellings associated to a graph. These generalize the Jukes-Cantor model and phylogenetic toric varieties defined by Buczy\'nska. Our main theorem bounds the degree of the generators of the semigroup by g+1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.
- Mathematics - Combinatorics
- Mathematics - Algebraic Geometry
- 20M14 (Primary) 14M25
- 14D21 (Secondary)