Proves that the square-root of Φ_p(G;x) yields a stronger DGS criterion than the square-free part via factorization into adjacency characteristic polynomials on the left null space of the walk matrix and its radical, enabling new DGS graph families via rooted products.
Wang, A simple arithmetic criterion for graphs being determined by their generalized spectra, J
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Factorization of invariant polynomials and generalized spectral characterizations of graphs
Proves that the square-root of Φ_p(G;x) yields a stronger DGS criterion than the square-free part via factorization into adjacency characteristic polynomials on the left null space of the walk matrix and its radical, enabling new DGS graph families via rooted products.