Geodesic
Arc-transitive groups of automorphisms of antipodal distance-regular graphs of diameter $3$ in affine case
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 445-495

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In this paper, we describe pairs $(\Gamma, G)$, where $\Gamma$ is an antipodal distance-regular graph of diameter $3$ that possesses an arc-transitive group of automorphisms $G$ such that $G$ induces an affine $2$-transitive permutation group on the set of its antipodal classes. As a corollary, we revise and specify a list of necessary conditions for existence of such pairs, and find several new additional necessary conditions in one-dimensional subcase.
Keywords: arc-transitive group, distance-regular graph
Mots-clés : antipodal cover, affine $2$-transitive group. 
@article{SEMR_2020_17_a63,
     author = {L. Yu. Tsiovkina},
     title = {Arc-transitive groups of automorphisms of antipodal distance-regular graphs of diameter $3$ in affine case},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {445--495},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a63/}
}
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L. Yu. Tsiovkina. Arc-transitive groups of automorphisms of antipodal distance-regular graphs of diameter $3$ in affine case. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 445-495. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a63/