Abstract
For a simple connected graph G of order n, the distance signless Laplacian matrix is defined by D-Q(G) = D(G) + Tr(G), where D(G) and Tr(G) is the distance matrix and the diagonal matrix of vertex transmission degrees, respectively. The zero divisor graph Gamma(R) of a finite commutative ring R is a simple graph, whose vertex set is the set of non-zero zero divisors of R and two vertices v, w is an element of Gamma(R) are edge connected whenever vw = wv = 0. In this article, we find the D-Q-eigenvalues of zero divisor graph of the ring Z(n) for general value n = p(1)(l1)p(2)(l2), where p(1) < p(2) are distinct prime numbers and l(1), l(2) is an element of N. Further, we investigate the D-Q-eigenvalues of zero divisor graphs of local rings and the rings whose associated zero divisor graphs are Hamiltonian. Also, we obtain the trace norm and the Wiener index of Gamma(Z(n)) for some special values of n.