Dipole graph
| Dipole graph | |
|---|---|
 | |
| Vertices | 2 |
| Edges | n |
| Diameter | 1 |
| Chromatic number | 2 |
| Chromatic index | n |
In graph theory, a dipole graph (or dipole) is a multigraph consisting of two vertices connected with a number of parallel edges. A dipole graph containing n edges is called the order-n dipole graph, and is denoted by Dn. The order-n dipole graph is dual to the cycle graph Cn.
The honeycomb as an abstract graph is the maximal abelian covering graph of the dipole graph D3, while the diamond crystal as an abstract graph is the maximal abelian covering graph of D4.
References
- Weisstein, Eric W., "Dipole Graph", MathWorld.
- Jonathan L. Gross and Jay Yellen, 2006. Graph Theory and Its Applications, 2nd Ed., p. 17. Chapman & Hall/CRC. ISBN 1-58488-505-X
- Sunada T., Topological Crystallography, With a View Towards Discrete Geometric Analysis, Springer, 2013, ISBN 978-4-431-54176-9 (Print) 978-4-431-54177-6 (Online)