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 graphCn.
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.
dipole, graph, graph, theory, dipole, graph, dipole, bond, graph, linkage, multigraph, consisting, vertices, connected, with, number, parallel, edges, dipole, graph, containing, edges, called, size, dipole, graph, denoted, size, dipole, graph, dual, cycle, gra. 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 Dipole graphVertices2EdgesnDiameter1 for n 1 Chromatic number2Chromatic indexnPropertiesconnected for n 1 planarTable of graphs and parametersThe 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 editWeisstein Eric W Dipole Graph MathWorld Jonathan L Gross and Jay Yellen 2006 Graph Theory and Its Applications 2nd Ed p 17 Chapman amp 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 nbsp This graph theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Dipole graph amp oldid 1214516698, wikipedia, wiki, book, books, library,
