[<< wikibooks] On 2D Inverse Problems/Triangulations of surfaces
Let G be a graph embedded to a surface such that all faces of G are triangular. Such an embedding is called triangulation.

Exercise (***). Generalize the examples to prove that the spectra of G* and M(G) are equal, except possibly the eigenvalue {6}.

σ
(

G

∗

)
∖
{
6
}
=
σ
(
M
(
G
)
)
∖
{
6
}

{\displaystyle \sigma (G^{*})\backslash \{6\}=\sigma (M(G))\backslash \{6\}}