Dipole graph
Multigraph with two vertices From Wikipedia, the free encyclopedia
In graph theory, a dipole graph, dipole, bond graph, or linkage, is a multigraph consisting of two vertices connected with a number of parallel edges. A dipole graph containing n edges is called the size-n dipole graph, and is denoted by Dn. The size-n dipole graph is dual to the cycle graph Cn.
 | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (November 2024) |
| Dipole graph | |
|---|---|
| |
| Vertices | 2 |
| Edges | n |
| Diameter | 1 (for n ≥ 1) |
| Chromatic number | 2 (for n ≥ 1) |
| Chromatic index | n |
| Properties | connected (for n ≥ 1) planar |
| Table of graphs and parameters | |
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.
Similarly to the Platonic graphs, the dipole graphs form the skeletons of the hosohedra. Their duals, the cycle graphs, form the skeletons of the dihedra.
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)
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