On the distance spectrum of cozero-divisor graph

For a commutative ring R with unity, the cozero-divisor graph denoted by Gamma ' (R), is an undirected simple graph whose vertex set is the set of all non-zero and non-unit elements of R. Two distinct vertices x and y are adjacent if and only if x does not belong to the ideal Ry and y does not belong to Rx. The cozero-divisor graph on the ring of integers modulo n is a generalized join of its induced sub graphs all of which are null graphs. This property of the cozero-divisor graph on Z(n) is used in finding its distance spectrum. In this paper, the distance matrix of the cozero-divisor graph on the ring of integers modulo n is discovered and the general method is discussed to find its distance spectrum, for any value of n. Also, the distance spectrum of this graph is explored for some values of n, by means of the vertex weighted distance matrix of the co-proper divisor graph of n.