[<< 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\}}