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FINITE NORMAL 2-GEODESIC TRANSITIVE CAYLEY GRAPHS
| Content Provider | Scilit |
|---|---|
| Author | Jin, Wei |
| Copyright Year | 2016 |
| Description | For an odd prime $p$ , a $p$ -transposition group is a group generated by a set of involutions such that the product of any two has order 2 or $p$ . We first classify a family of $(G,2)$ -geodesic transitive Cayley graphs ${\rm\Gamma}:=\text{Cay}(T,S)$ where $S$ is a set of involutions and $T:\text{Inn}(T)\leq G\leq T:\text{Aut}(T,S)$ . In this case, $T$ is either an elementary abelian 2-group or a $p$ -transposition group. Then under the further assumption that $G$ acts quasiprimitively on the vertex set of ${\rm\Gamma}$ , we prove that: (1) if ${\rm\Gamma}$ is not $(G,2)$ -arc transitive, then this quasiprimitive action is the holomorph affine type; (2) if $T$ is a $p$ -transposition group and $S$ is a conjugacy class, then $p=3$ and ${\rm\Gamma}$ is $(G,2)$ -arc transitive. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FC602D7E5C7C0DF2051223FD7D67555F/S1446788715000786a.pdf/div-class-title-finite-normal-2-geodesic-transitive-cayley-graphs-div.pdf |
| Ending Page | 348 |
| Page Count | 11 |
| Starting Page | 338 |
| ISSN | 14467887 |
| e-ISSN | 14468107 |
| DOI | 10.1017/s1446788715000786 |
| Journal | Journal of the Australian Mathematical Society |
| Issue Number | 3 |
| Volume Number | 100 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2016-06-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society Mathematical Physics Primary 05e18 Secondary 20b25 geodesic Transitive Graph Cayley Graph Automorphism Group |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
