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Distance-regular Cayley graphs with small valency
| Content Provider | Semantic Scholar |
|---|---|
| Author | Dam, Edwin R. Van Jazaeri, Mojtaba |
| Copyright Year | 2018 |
| Abstract | We consider the problem of which distance-regular graphs with small valency are Cayley graphs. We determine the distance-regular Cayley graphs with valency at most $4$, the Cayley graphs among the distance-regular graphs with known feasible intersection arrays for valency $5$, and the Cayley graphs among all distance-regular graphs with girth $3$ and valency $6$ or $7$. We obtain that the incidence graphs of Desarguesian affine planes minus a parallel class of lines are Cayley graphs. We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons. Among some "exceptional" distance-regular graphs with small valency, we find that the Armanios-Wells graph and the Klein graph are Cayley graphs. |
| File Format | PDF HTM / HTML |
| DOI | 10.26493/1855-3974.1964.297 |
| Alternate Webpage(s) | https://amc-journal.eu/index.php/amc/article/download/1964/1448 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1808.01428v2.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
