Chip-firing on trees of loops (Q1700782)

Summary: \textit{F. Cools} et al. [Adv. Math. 230, No. 2, 759--776 (2012; Zbl 1325.14080)] proved that generic metric graphs that are ``paths of loops'' are Brill-Noether general. We show that Brill-Noether generality does not hold for ``trees of loops'': the only trees of loops that are Brill-Noether general are paths of loops. We study various notions of generality and examine which of these graphs satisfy them.