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

Abstract

A Schrödinger operator and associated spectra may be defined for a graph by identifying edges with intervals of , 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