Dipole graph
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Wikipedia : http://en.wikipedia.org/wiki/Dipole_graphDipole graph | |
---|---|
Vertices | 2 |
Edges | |
Diameter | 1 (for ) |
Chromatic number | 2 |
Chromatic index | |
Properties |
connected (for ) planar |
In graph theory, a dipole graph (also called a dipole or bond graph) 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 D_{n}. The order-n dipole graph is dual to the cycle graph C_{n}.
The honeycomb as an abstract graph is the maximal abelian covering graph of the dipole graph D_{3}, while the diamond crystal as an abstract graph is the maximal abelian covering graph of D_{4}.
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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