Geodesic
Arc-transitive distance-regular coverings of cliques with $\lambda=\mu$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 237-246 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study antipodal distance-regular graphs of diameter 3 such that their group of automorphisms acts transitively on the set of pairs $(a,b)$, where $\{a,b\}$ is an edge of the graph. Hence the group of automorphisms of the graph acts $2$-transitively on the set of antipodal classes, so the classification of $2$-transitive permutation groups can be used. We classify arc-transitive distance-regular graphs of diameter 3 in which any two vertices with distance at most two have exactly $\mu$ common neighbors.
Keywords: arc-transitive graphs, antipodal distance-regular graphs, groups of automorphisms. 
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A. A. Makhnev; D. V. Paduchikh; L. Yu. Tsiovkina. Arc-transitive distance-regular coverings of cliques with $\lambda=\mu$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 237-246. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a22/

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