  Let $k,l,m,n$, and $\mu$ be positive integers. A $\mathbb{Z}_\mu$--{\it
scheme of valency} $(k,l)$ and {\it order} $(m,n)$ is a $m \times n$ array
$(S_{ij})$ of subsets $S_{ij} \subseteq \mathbb{Z}_\mu$ such that for each row
and column one has $\sum_{j=1}^n |S_{ij}| = k $ and $\sum_{i=1}^m |S_{ij}| =
l$, respectively. Any such scheme is an algebraic equivalent of a
$(k,l)$-semi-regular bipartite voltage graph with $n$ and $m$ vertices in the
bipartition sets and voltages coming from the cyclic group $\mathbb{Z}_\mu$. We
are interested in the subclass of $\mathbb{Z}_\mu$--schemes that are
characterized by the property $a - b + c - d\; \not \equiv \;0$ (mod $\mu$) for
all $a \in S_{ij}$, $b \in S_{ih}$, $c \in S_{gh}$, and $d \in S_{gj}$ where
$i,g \in {1,...,m}$ and $j,h \in {1,...,n}$ need not be distinct. These
$\mathbb{Z}_\mu$--schemes can be used to represent adjacency matrices of
regular graphs of girth $\ge 5$ and semi-regular bipartite graphs of girth $\ge
6$. For suitable $\rho, \sigma \in \mathbb{N}$ with $\rho k = \sigma l$, they
also represent incidence matrices for polycyclic $(\rho \mu_k, \sigma \mu_l)$
configurations and, in particular, for all known Desarguesian elliptic
semiplanes. Partial projective closures yield {\it mixed
$\mathbb{Z}_\mu$-schemes}, which allow new constructions for Kr\v{c}adinac's
sporadic configuration of type $(34_6)$ and Balbuena's bipartite
$(q-1)$-regular graphs of girth 6 on as few as $2(q^2-q-2)$ vertices, with $q$
ranging over prime powers. Besides some new results, this survey essentially
furnishes new proofs in terms of (mixed) $\mathbb{Z}_\mu$--schemes for ad-hoc
constructions used thus far.
