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| Content Provider | Springer Nature Link |
|---|---|
| Author | Yang, DaWei Feng, YanQuan |
| Copyright Year | 2016 |
| Abstract | A graph is symmetric or 1-regular if its automorphism group is transitive or regular on the arc set of the graph, respectively. We classify the connected pentavalent symmetric graphs of order 2p $^{3}$ for each prime p. All those symmetric graphs appear as normal Cayley graphs on some groups of order 2p $^{3}$ and their automorphism groups are determined. For p = 3, no connected pentavalent symmetric graphs of order 2p $^{3}$ exist. However, for p = 2 or 5, such symmetric graph exists uniquely in each case. For p ≥ 7, the connected pentavalent symmetric graphs of order 2p $^{3}$ are all regular covers of the dipole Dip5 with covering transposition groups of order p $^{3}$, and they consist of seven infinite families; six of them are 1-regular and exist if and only if 5 | (p-1), while the other one is 1-transitive but not 1-regular and exists if and only if 5 | (p± 1). In the seven infinite families, each graph is unique for a given order. |
| Starting Page | 1851 |
| Ending Page | 1868 |
| Page Count | 18 |
| File Format | |
| ISSN | 16747283 |
| Journal | Science in China Series A: Mathematics |
| Volume Number | 59 |
| Issue Number | 9 |
| e-ISSN | 18691862 |
| Language | English |
| Publisher | Science China Press |
| Publisher Date | 2016-04-07 |
| Publisher Place | Beijing |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Cayley graph symmetric graph regular cover Applications of Mathematics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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