Consider two graphs G 1 and G 2 having 20 nodes each. Both of the graphs have a common Laplacian eigenvalue 4.5, which also is the largest Laplacian eigenvalue of G 2. Is it possible to find a signal defined on graph G 2 that has a 2-Dirichlet form value greater than 2-Dirichlet form of the eigenvector corresponding to the eigenvalue 4.5? Is it possible to find such signal defined on graph G 1 ?
Note: There is a small error in the problem mentioned in the book. This is the correct version.
If the graph G1 has a Laplacian eigenvalue greater that 4.5, then it is possible to define a
signal on G1 to have its 2-Dirichlet form greater than 4.5, otherwise not.
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