Exploring normalized distance Laplacian eigenvalues of the zero-divisor graph of ring Zn.

In this paper, we investigate the normalized distance Laplacian spectrum of the zero-divisor graph of a commutative ring R , denoted by Γ (R) , where R is taken as the ring of integers modulo n. The graph has vertex set Z (R) ∗ , which is the set of nonzero zero-divisors of R , and two vertices x and y are connected by an edge if and only if x y = 0 . Specifically, we analyze the normalized distance Laplacian spectrum of Γ (Z n) , where n = p S q T , p and q are primes with p < q , and S and T are positive integers. [ABSTRACT FROM AUTHOR]