Spectral characterization of the uniform theta graph $Θ(t,2)$ and classification of 6-periodic Grover walks

We characterize the uniform theta graph $Θ(t,2)$ by the spectrum of its normalized adjacency matrix, or equivalently, by the spectrum of its normalized Laplacian matrix. We also investigate the periodicity of Grover walks on nonregular graphs, which is closely related to the eigenvalues of the norma