Geodesic
Construction of Cospectral Integral Regular Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 595-609

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Graphs G and H are called cospectral if they have the same characteristic polynomial. If eigenvalues are integral, then corresponding graphs are called integral graph. In this article we introduce a construction to produce pairs of cospectral integral regular graphs. Generalizing the construction of G_4(a, b) and G_5(a, b) due to Wang and Sun, we define graphs 𝒢_4(G,H) and 𝒢_5(G,H) and show that they are cospectral integral regular when G is an integral q-regular graph of order m and H is an integral q-regular graph of order (b − 2)m for some integer b ≥ 3.
Keywords: eigenvalue, cospectral graphs, adjacency matrix, integral graphs 
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Bapat, Ravindra B.; Karimi, Masoud. Construction of Cospectral Integral Regular Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 595-609. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a7/