  We study the correspondence assigning the vertices of a certain quotient of
the local Bruhat-Tits tree for the general linear group over a global function
field, to conjugacy classes of maximal orders in some quaternion algebras. The
interplay between quotient graphs and orders can be used to study
representation of orders if the quotient graphs are known and conversely. We
use this converse to find a reciprocity law between quotient graph at diferent
places that suffices to compute, recursively, all local quotient graphs for a
matrix algebra over a rational function field.
