User:DVD206/"Can One Hear the Shape of a Drum?"

Let $\lambda _{k}$ be the Dirichlet eigenvalues for the domain $\Omega$, that is, the eigenvalues of the Dirichlet problem for the Laplacian:

${\begin{cases}\Delta u+\lambda u=0,\\u|_{\partial \Omega }=0.\end{cases}}$

Since the system above is self-adjoint, the eigenvalues are positive. Two domains are said to be isospectral if they have the same Laplacian eigenvalues.

One can state the discrete analog of the question on graphs...