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Let $G$ and $H$ be two cospectral graphs, then can we say that their adjacency matrices are isomorphic?

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    $\begingroup$ They are similar by orthogonal transformation, what do you mean by isomorphism? $\endgroup$
    – Fedor Petrov
    Commented Sep 27, 2016 at 19:53
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    $\begingroup$ If by isomorphic adjacency, you mean these two graphs must be isomorphic, your answer is no. But you must give clear definition of "isomorphic adjacency matrices". $\endgroup$
    – Shahrooz
    Commented Sep 27, 2016 at 23:03
  • $\begingroup$ Relevant: yasser could get a suggestion from this thread. $\endgroup$
    – Peter Heinig
    Commented Aug 28, 2017 at 20:51

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