What does the spectrum of the adjacency matrix of a graph tell you?

Asked Dec 14 '15 at 06:37

Active Dec 14 '15 at 06:37

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I am trying to search for an answer to the following question and I cannot find a straightforward answer.

What does the spectrum of the adjacency matrix (set of eigenvalues and their multiplicities) of a graph tell you about the structure of a graph?

Thank you!

asked Dec 14 '15 at 06:37

Stefos

1

I would guess that you will get more information out of the coefficients of the characteristic polynomial, which encode the same information but are integers, hence easier to work with. There are various results about this graph invariant, such as formulas for the coefficients in terms of certain cycle counts. – Andrew Dudzik Dec 14 '15 at 06:50

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