Prove that the GFT associated with a Cartesian product graph is given by the matrix Kro- necker product of the GFTs for its factor graphs (use weight matrix as shift operator). Also comment on the spectrum of the Cartesian product graph. Verify your results for the Cartesian product of the two graphs given in Figure 10.4. You can choose any values for the signals defined on the graphs. Hint: Refer to Section 2.5.9 for the definitions of product graphs.

What will be an ideal response?

Therefore, the graph Fourier transform matrix is given by





The spectrum of the product graph is the element-wise summation of the spectra of the


smaller graphs.