Nonbacktracking spectrum and surprises in non-regular graphs

Joel Friedman
University of British Columbia

We show that the nonbacktracking spectrum of non-regular graphs can be two dimensional as a subset of the complex plane. This promises to make life difficult but interesting for formulating notions of Ramanujan graphs for non-regular graphs, the generalized Alon conjecture, etc. This is joint work with Omer Angel and Shlomo Hoory.

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