Suppose you have two adjacency matrices $A$ and $B$ of cospectral but non-isomorphic graphs. Is there a matrix $Q$ such that $$A=Q^{-1}BQ$$ holds?
Note if $A$ and $B$ are not cospectral we cannot have a $Q$ such that $$A=Q^{-1}BQ$$ holds.
2026-03-26 21:12:43.1774559563
Are cospectral/non-cospectral non-isomorphic graphs similar?
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Two real symmetric matrices are similar if and only if they have the same characteristic polynomial. So if two graphs are cospectral, their adjacency matrices must be similar.