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arXiv · 1808.01428

Distance-regular Cayley graphs with small valency

Edwin R. van Dam·Mojtaba Jazaeri
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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.

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Edwin R. van Dam, Mojtaba Jazaeri. 2018-08-04. Distance-regular Cayley graphs with small valency. https://arxiv.org/abs/1808.01428

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