Normalized Laplacian Spectrum of Some Q-Coronas of Two Regular Graphs

In this paper we determine the normalized Laplacian spectrum of the Q-vertex corona, Q-edge corona, Q-vertex neighborhood corona, and Q-edge neighborhood corona of a connected regular graph with an arbitrary regular graph in terms of normalized Laplacian eigenvalues of the original graphs. Moreover, applying these results we find some non-regular normalized Laplacian co-spectral graphs.