Inverse eigenvalue problems on directed graphs

Abstract

The differential operators i D iD and − D 2 − p -D^2 - p are constructed on certain finite directed weighted graphs. Two types of inverse spectral problems are considered. First, information about the graph weights and boundary conditions is extracted from the spectrum of − D 2 -D^2 . Second, the compactness of isospectral sets for − D 2 − p -D^2 - p is established by computation of the residues of the zeta function.