Name
Abstract | ||
|---|---|---|
A directed Cayley graph X is called a digraphical regular representation (DRR) of a group G if the automorphism group of X acts regularly on X. Let S be a finite generating set of the infinite cyclic group Z. We show that a directed Cayley graph X(Z, S) is a DRR of Z if and only if S not equal S-1. If X (Z, S) is not a DRR we show that Aut (X(Z, S)) = D-infinity,. As a general result we prove that a Cayley graph X of a finitely generated torsion-free nilpotent group N is a DRR if and only if no non-trivial automorphism of N of finite order leaves the generating set invariant. (C) 1998 Academic Press. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1006/eujc.1998.0210 | Eur. J. Comb. |
Keywords | Field | DocType |
digraphical regular representation,infinite finitely | Stallings theorem about ends of groups,Combinatorics,Regular representation,Automorphism,Generating set of a group,Cayley transform,Cayley graph,Inner automorphism,Mathematics,Nilpotent | Journal |
Volume | Issue | ISSN |
19 | 5 | 0195-6698 |
Citations | PageRank | References |
1 | 0.37 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rögnvaldur G. Möller | 1 | 35 | 6.28 |
| N Seifter | 2 | 137 | 26.49 |