“Dipole graph”的意思、由来-开放百科全书

词条

Dipole graph

释义

References

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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 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

{{MathWorld|title = Dipole Graph|urlname = DipoleGraph}}
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)

3 : Extensions and generalizations of graphs|Parametric families of graphs|Regular graphs

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