The conjecture that breaking all non-trivial graph automorphisms suffices for universality in globally controlled qubit systems is disproved by connected graphs with trivial automorphism groups whose generated Lie algebras are nonetheless non-universal.
Lloyd, A potentially realizable quantum computer, Science 261, 1569 (1993)
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Obstructions to universality in globally controlled qubit graphs
The conjecture that breaking all non-trivial graph automorphisms suffices for universality in globally controlled qubit systems is disproved by connected graphs with trivial automorphism groups whose generated Lie algebras are nonetheless non-universal.