On cospectral graphons

Jan Hladký, Daniel Iľkovič, Jared León, Xichao Shu

Published 2024-11-20Version 1

In this short note, we introduce cospectral graphons, paralleling the notion of cospectral graphs. As in the graph case, we give three equivalent definitions: by equality of spectra, by equality of cycle densities, and by a unitary transformation. We also give an example of two cospectral graphons that cannot be approximated by two sequences of cospectral graphs in the cut distance.