Voltage graph

A voltage graph is a concise way to specify a regular digraph

[edit] Formal Definition

Formally:

A $\mathbb{Z}_{n}$ -voltage on an arc of a digraph $G$ is a label by a number $i (mod n)$
A $\mathbb{Z}_{n}$ -voltage assignment is a function $\alpha : E_{G} \rightarrow \mathbb{Z}_{n}$ that labels each arc on a digraph $G$ with a $\mathbb{Z}_{n}$ -voltage
A $\mathbb{Z}_{n}$ -voltage graph (or cyclic-voltage graph) is a pair $\langle G, \alpha: E_{G} \rightarrow \mathbb{Z}_{n} \rangle$ such that $G$ is a digraph and $α$ is a voltage assignment
The voltage group of a voltage graph $\langle G, \alpha: E_{G} \rightarrow \mathbb{Z}_{n} \rangle$ is the group $\mathbb{Z}_{n}$ from which the voltages are assigned.