Inverse eigenvalue problem for a simple star graph

  • William Rundell

    Texas A&M University, College Station, United States
  • Paul Sacks

    Iowa State University, Ames, USA


A Schrödinger operator and associated spectra may be defined for a graph by identifying edges with intervals of R\mathbb R, on which coefficient functions are defined, imposing appropriate matching conditions at the internal vertices and boundary conditions at the external vertices. Following earlier work of Pivovarchik [14], we consider an inverse eigenvalue problem for a graph consisting of three equal length edges meeting at a single point, where the spectral data is the Dirichlet eigenvalues of the graph together with the Dirichlet spectra of the three individual edges. We derive, discuss and demonstrate a constructive solution method, obtain an alternative uniqueness proof, and discuss several kinds of generalizations.

Cite this article

William Rundell, Paul Sacks, Inverse eigenvalue problem for a simple star graph. J. Spectr. Theory 5 (2015), no. 2, pp. 363–380

DOI 10.4171/JST/101