On distance Laplacian spectrum of zero divisor graphs of the ring Zn

For a finite commutative ring Z(n) with identity 1 not equal 0, the zero divisor graph Gamma(Z(n)) is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices x and y are adjacent if and only if xy = 0. We find the distance Laplacian spectrum of the zero divisor graphs Gamma(Z(n)) for different values of n. Also, we obtain the distance Laplacian spectrum of Gamma(Z(n)) for n = p(z), z >= 2, in terms of the Laplacian spectrum. As a consequence, we determine those n for which zero divisor graph Gamma(Z(n)) is distance Laplacian integral.