Abstract
We study the Laplacian eigenvalues of the zero divisor graph Γ(Zn) of the ring Zn and prove that Γ(Zpt) is Laplacian integral for every prime p and positive integer t≥2. We also prove that the Laplacian spectral radius and the algebraic connectivity of Γ(Zn) for most of the values of n are, respectively, the largest and the second smallest eigenvalues of the vertex weighted Laplacian matrix of a graph which is defined on the set of proper divisors of n. The values of n for which algebraic connectivity and vertex connectivity of Γ(Zn) coincide are also characterized.
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