  A graph is said to be globally rigid if almost all embeddings of the graph's
vertices in the Euclidean plane will define a system of edge-length equations
with a unique (up to isometry) solution. In 2007, Jackson, Servatius and
Servatius characterised exactly which vertex-transitive graphs are globally
rigid solely by their degree and maximal clique number, two easily computable
parameters for vertex-transitive graphs. In this short note we will extend this
characterisation to all graphs that are determined by their automorphism group.
We do this by characterising exactly which edge-transitive graphs and
distance-regular graphs are globally rigid by their minimal and maximal
degrees.
