# Eigenvectors of asymmetric graphs

Let $G$ be an asymmetric connected graph. Then is it always the case that at least one of the eigenvectors of its adjacency matrix $A$ consists entirely of distinct entries?

Thanks!

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By asymmetric, you mean the automorphism group is trivial? –  Douglas Zare Aug 8 '12 at 18:44
Yes, the graph has a trivial automorphism group. And yes I'm assuming a connected graph. I edited the question to reflect this. –  Alexander Farrugia Aug 9 '12 at 6:23
I'm curious what was the motivation for the question. –  Felix Goldberg Aug 9 '12 at 12:42