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- W4289709056 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 putative 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." @default.
- W4289709056 created "2022-08-04" @default.
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- W4289709056 date "2018-08-04" @default.
- W4289709056 modified "2023-09-25" @default.
- W4289709056 title "Distance-regular Cayley graphs with small valency" @default.
- W4289709056 doi "https://doi.org/10.48550/arxiv.1808.01428" @default.
- W4289709056 hasPublicationYear "2018" @default.
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