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Automorphism Groups of Metacirculant Graphs of Order a Product of Two Distinct Primes
| Content Provider | Scilit |
|---|---|
| Author | Dobson, Edward |
| Copyright Year | 2006 |
| Description | Let p and q be distinct primes. We characterize transitive groups G that admit a complete block system of q blocks of size p such that the subgroup of G which fixes each block set-wise has a Sylow p-subgroup of order p. Using this result, we prove that the full automorphism group of a metacirculant graph Γ of order pq such that Aut(Γ) is imprimitive, is contained in one of several families of transitive groups. As the automorphism groups of vertex-transitive graphs of order pq that are primitive have been determined by several authors, this result implies that automorphism groups of vertex-transitive graphs of order pq are known. We also determine all nonnormal Cayley graphs of order pq, and all 1/2-transitive graphs of order pq. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/8E6F53E730F707811F3CB9EA16CD9293/S0963548305007066a.pdf/div-class-title-automorphism-groups-of-metacirculant-graphs-of-order-a-product-of-two-distinct-primes-div.pdf |
| Ending Page | 130 |
| Page Count | 26 |
| Starting Page | 105 |
| ISSN | 09635483 |
| e-ISSN | 14692163 |
| DOI | 10.1017/s0963548305007066 |
| Journal | Combinatorics, Probability and Computing |
| Issue Number | 1-2 |
| Volume Number | 15 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2006-01-01 |
| Access Restriction | Open |
| Subject Keyword | Combinatorics, Probability and Computing Literary Studies Complete Block System Automorphism Group Transitive Group wise Order Pq Full Automorphism Group Metacirculant Graphs Order P Automorphism Groups Size P Distinct Primes Q Block transitive Graph |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics |
