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One-regular cubic graphs of order a small number times a prime or a prime square
| Content Provider | Scilit |
|---|---|
| Author | Feng, Yan-Quan Kwak, Jin Ho |
| Copyright Year | 2004 |
| Description | A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper we show that there exists a one-regular cubic graph of order 2p or $2p^{2}$ where p is a prime if and only if 3 is a divisor of p – 1 and the graph has order greater than 25. All of those one-regular cubic graphs are Cayley graphs on dihedral groups and there is only one such graph for each fixed order. Surprisingly, it can be shown that there is no one-regular cubic graph of order 4p or $4p^{2}$. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F2C33C0FB540F6517453CC539981AA6D/S1446788700009903a.pdf/div-class-title-one-regular-cubic-graphs-of-order-a-small-number-times-a-prime-or-a-prime-square-div.pdf |
| Ending Page | 356 |
| Page Count | 12 |
| Starting Page | 345 |
| ISSN | 14467887 |
| e-ISSN | 14468107 |
| DOI | 10.1017/s1446788700009903 |
| Journal | Journal of the Australian Mathematical Society |
| Issue Number | 3 |
| Volume Number | 76 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2004-06-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society Applied Mathematics Primary 05c25 Cayley Graph transitive Graph regular Graph |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
