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Vertex-primitive groups and graphs of order twice the product of two distinct odd primes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gamble, Greg |
| Abstract | A non-Cayley number is an integer n for which there exists a vertex-transitive graph on n vertices which is not a Cayley graph. In this paper, we complete the determination of the nonCayley numbers of the form 2pq, where p; q are distinct odd primes. Earlier work of Miller and the second author had dealt with all such numbers corresponding to vertex-transitive graphs admitting an imprimitive subgroup of automorphisms. This paper deals with the primitive case. First the primitive permutation groups of degree 2pq are classi®ed. This depends on the ®nite simple group classi®cation. Then each of these groups G is examined to determine whether there are any non-Cayley graphs which admit G as a vertex-primitive subgroup of automorphisms, and admit no imprimitive subgroups. The outcome is that 2pq is a non-Cayley number, where 2 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://espace.library.uq.edu.au/data/UQ_141657/UQ141657_OA.pdf?Expires=1541657857&Key-Pair-Id=APKAJKNBJ4MJBJNC6NLQ&Signature=OUa68AG5BSXAh~uAboOCrGlU5YzLcs6zTot-f0YX8~0pLlhOuSQ2XBeXIDW2ZrAiN8Z5rPZgR3gUGj7am8cA6ZB4dhgwWOM2XxLzzSMEALYB2SpHytv4DW7Up8w6ljBwaOilOKaggiiqXc3HlFWmhInn2ypXv~1VsKpwWsvlEcYsGbWuOADo2dWO3OCpUj5tNGKI~ceVGt-HAjc8XgPFUWMN58P6OZNQS5uubUrszCbQrcatbXltUZqgqDM38u8u8ChupCQwcJiu0Ps87k-o9c54jEDfLe0R5fpj4weNXeaEA2qVRUuzBw4-M1viT-LL3jHyfmBeaJkKE3ulAGUVGg__ |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Cations Graph - visual representation Hospital admission Integer (number) Isogonal figure Magma Mod Database Subgroup A Nepoviruses Vertex Vertex-transitive graph |
| Content Type | Text |
| Resource Type | Article |
