  Synchronization in networks of interconnected oscillators is a fascinating
phenomenon that appear naturally in many independent fields of science and
engineering. A substantial amount of work has been devoted to understanding all
possible synchronization configurations on a given network. In this setting, a
key problem is to determine the total number of such configurations. Through an
algebraic formulation, for tree and cycle graphs, we provide an upper bound on
this number using the birationally invariant intersection index of a system of
rational functions on a toric variety.
