Spectra of some interesting combinatorial matrices related to oriented spanning trees on a directed graph (Q1906249)

For a digraph \(G\) let \(D(G)\) be the digraph whose vertices are all oriented rooted spanning trees of \(G\) with arcs connecting vertices corresponding to oriented rooted spanning trees which can be obtained one from the other by a local transformation defined in the paper. The author relates eigenvalues of \(D(G)\) to eigenvalues of induced subgraphs of \(G\) and to Laplacian eigenvalues of \(G\).