Geodesic
Normalized Laplacian Spectrum of Some Q-Coronas of Two Regular Graphs
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 127-138

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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.
Keywords: normalized Laplacian matrix, Q -vertex corona, Q -edge corona, Q -vertex neighborhood corona, Q -edge neighborhood corona, Kronecker product, Hadamard product 
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Das, Arpita; Panigrahi, Pratima. Normalized Laplacian Spectrum of Some Q-Coronas of Two Regular Graphs. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 127-138. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a10/