TY  - JOUR
ID  - Dudko2024
LB  - Dudko2024
AU  - Dudko, Anastasia
AU  - Lesechko, Oleksandr
AU  - Pivovarchik, Vyacheslav
TI  - Recovering the shape of an equilateral quantum tree with the Dirichlet conditions at the pendant vertices
ST  - Recovering the shape of an equilateral quantum tree with the Dirichlet conditions at the pendant vertices
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 5
SP  - 689
EP  - 705
DO  - https://doi.org/10.7494/OpMath.2024.44.5.689
UR  - https://doi.org/10.7494/OpMath.2024.44.5.689
AB  - We consider two spectral problems on an equilateral rooted tree with the standard (continuity and Kirchhoff's type) conditions at the interior vertices (except of the root if it is interior) and Dirichlet conditions at the pendant vertices (except of the root if it is pendant). For the first (Neumann) problem we impose the standard conditions (if the root is an interior vertex) or Neumann condition (if the root is a pendant vertex) at the root, while for the second (Dirichlet) problem we impose the Dirichlet condition at the root. We show that for caterpillar trees the spectra of the Neumann problem and of the Dirichlet problem uniquely determine the shape of the tree. Also, we present an example of co-spectral snowflake graphs.
KW  - Sturm-Liouville equation
KW  - eigenvalue
KW  - spectrum
KW  - equilateral tree
KW  - caterpillar tree
KW  - snowflake graph
KW  - root
KW  - standard conditions
KW  - Dirichlet boundary condition
KW  - Neumann boundary condition
SN  - 1232-9274
ER  -