I know that the spectrum of the adjacency matrix enumerates the number of closed walks, and the spectrum of the reduced laplacian enumerates the number of spanning trees. Does being both adjacency and laplacian cospectral imply that the degree sequences are the same? Has anyone proved this before, or does there exist a counter example?
2026-03-25 14:20:54.1774448454
Do Adjacency and Laplacian cospectral graphs always have the same degree sequence?
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