Name
Abstract | ||
|---|---|---|
We study regular maps with nilpotent automorphism groups in detail. We prove that every nilpotent regular map decomposes into a direct product of maps HxK, where Aut(H) is a 2-group and K is a map with a single vertex and an odd number of semiedges. Many important properties of nilpotent maps follow from this canonical decomposition, including restrictions on the valency, covalency, and the number of edges. We also show that, apart from two well-defined classes of maps on at most two vertices and their duals, every nilpotent regular map has both its valency and covalency divisible by 4. Finally, we give a complete classification of nilpotent regular maps of nilpotency class 2. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.ejc.2012.06.001 | Eur. J. Comb. |
Keywords | Field | DocType |
complete classification,nilpotent map,nilpotent regular map,covalency divisible,regular map,canonical decomposition,odd number,maps hxk,nilpotent regular map decomposes,nilpotent automorphism group | Discrete mathematics,Combinatorics,Direct product,Nilpotent group,Vertex (geometry),Valency,Automorphism,Dual polyhedron,Regular map,Mathematics,Nilpotent | Journal |
Volume | Issue | ISSN |
33 | 8 | 0195-6698 |
Citations | PageRank | References |
1 | 0.38 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Aleksander Malnic | 1 | 324 | 31.54 |
| Roman Nedela | 2 | 392 | 47.78 |
| Martin Škoviera | 3 | 427 | 54.90 |