Median eigenvalues of subcubic graphs

Abstract

We show that the median eigenvalues of every connected graph of maximum degree at most three, except for the Heawood graph, are at most $1$ in absolute value, resolving open problems posed by Fowler and Pisanski, and by Mohar.

59 pages, 9 figures and 167 diagrams; revised version expands several results to subcubic graphs, adds ancillary Lean formalization, and corrects several minor omissions in the lengthy case analysis