Suppose that Τπ(Zp1p2...pα) is a graph with the vertex set of nonzero zero-divisors of the finite ring Zp1p2...pα, where α > 1, and x - y is an edge if and only if x and y are π-prime, where π = fp1,p2..., pαg is a set of odd prime numbers and a and b are π-prime if either (a; b) = 1 or (a; b) = p, p = π. In this paper we study dimension, edge metric dimension and fraction dimension of the graph.