  In this paper, we continue investigation of the directed and undirected
irreducible divisor graph concepts $G(x)$ and $\Gamma (x)$ of $x\in D^{\ast}
\backslash U(D)$, respectively, which were introduced in [7]. Consequently, we
introduce two generalizations of these concepts. The first one is the
irreducible divisor simplicial complex $S(x)$ of $x\in D^{\ast} \backslash
U(D)$ in a noncommutative atomic domain $D$, which simultaneously extends the
commutative case that was introduced by R. Baeth and J. Hobson in [3]. The
second one is the directed and undirected $\tau $-irreducible divisor graphs
$G_{\tau }(x)$ and $\Gamma _{\tau }(x)$ of $x\in D^{\ast} \backslash U(D)$,
respectively, in a noncommutative $\tau $-atomic domain $D$ with a symmetric
and associate preserving relation $\tau $ on $D^{\ast} \backslash U(D)$. Those
graphs also extend the commutative case that was introduced by C. P. Mooney in
[5]. Furthermore, we extend the results of [3] and [5] to give a
characterization of n-unique factorization domains via those two
generalizations.
