Voltage graph

Article summary

In graph theory, a voltage graph is a directed graph whose edges are labelled invertibly by elements of a group. It is formally identical to a gain graph, but it is generally used in topological graph theory as a concise way to specify another graph called the derived graph of the voltage graph. Typical choices of the groups used for voltage graphs include the two-element group \mathbb{Z}_2 (for defining the bipartite double cover of a graph), free groups (for defining the universal cover of a graph), d-dimensional integer lattices \mathbb{Z}^d (viewed as a group under vector addition, for defining periodic structures in d-dimensional Euclidean space), and finite cyclic groups \mathbb{Z_n} for n > 2. When is a cyclic group, the voltage graph may be called a cyclic-voltage graph.

Key claims

No claims recorded.

Discussion questions

1. Summarise the article in your own words. Which single claim would you verify first, and why?
2. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

No sources recorded.