The spectral analysis of the unitary matrix of a 2-tessellable staggered quantum walk on a graph

Recently, the staggered quantum walk (SQW) on a graph is discussed as a generalization of coined quantum walks on graphs and Szegedy walks. We present a formula for the characteristic polynomial of the time evolution matrix of a 2-tessellable SQW on a graph, and so directly give its spectra. Furthermore, we discuss about the property of the eigenvalues of the discriminant for the time evolution matrix of a 2-tessellable SQW on a graph, and present eigenvectors for some of its eigenvalues.