Name
Abstract | ||
|---|---|---|
We show that if n=p^e where p is an odd prime and e=1, then the complete bipartite graph K"n","n has p^e^-^1 regular embeddings in orientable surfaces. These maps, which are Cayley maps for cyclic and dihedral groups, have type {2n,n} and genus (n-1)(n-2)/2; one is reflexible, and the rest are chiral. The method involves groups which factorise as a product of two cyclic groups of order n. We deduce that if n is odd then K"n","n has at least n/@?"p"|"np orientable regular embeddings, and that this lower bound is attained if and only if no two primes p and q dividing n satisfy p=1mod(q). |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.ejc.2005.07.021 | Eur. J. Comb. |
Keywords | Field | DocType |
order n,dihedral group,regular embeddings,cyclic group,cayley map,np orientable regular embeddings,primes p,odd prime power,complete bipartite graph k,orientable surface,complete bipartite graph,satisfiability,lower bound | Prime (order theory),Discrete mathematics,Complete bipartite graph,Combinatorics,Cyclic group,Dihedral group,Upper and lower bounds,Prime power,Mathematics | Journal |
Volume | Issue | ISSN |
28 | 6 | 0195-6698 |
Citations | PageRank | References |
16 | 1.44 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gareth A. Jones | 1 | 116 | 23.18 |
| Roman Nedela | 2 | 392 | 47.78 |
| Martin Škoviera | 3 | 427 | 54.90 |