The main concept of this part of the paper is that of a reduced exponent matrix and its quiver, which is strongly connected and simply laced. We give the description of quivers of reduced Gorenstein exponent matrices whose number s of vertices is at most 7. For 2 6 s 6 5 we have that all adjacency matrices of such quivers are multiples of doubly stochastic matrices. We prove that for any permutation σ on n letters without fixed elements there exists a reduced Gorenstein tiled order ¤ with σ(E) = σ. We show that for any positive integer k there exists a Gorenstein tiled order ¤k with in¤k = k. The adjacency matrix of any cyclic Gorenstein order ¤ is a linear combination of powers of a permutation matrix P¾ with non-negative coefficients, where σ = σ(¤). If A is a noetherian prime semiperfect semidistributive ring of a finite global dimension, then Q(A) be a strongly connected simply laced quiver which has no loops.