Geodesic
Arc-transitive antipodal distance-regular graphs of diameter three related to~$PSL_d(q)$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1339-1345

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In this paper, we investigate antipodal distance-regular graphs of diameter three and valency $q(q^{d-1}-1)/(q-1)$ with arc-transitive automorphism group which induces an almost simple permutation group on the antipodal classes with the socle isomorphic to $PSL_d(q),$ where $ d\ge 3$. We find that such a graph is necessarily bipartite.
Keywords: arc-transitive graph, distance-regular graph
Mots-clés : antipodal cover. 
@article{SEMR_2016_13_a42,
     author = {A. A. Makhnev and L. Yu. Tsiovkina},
     title = {Arc-transitive antipodal distance-regular graphs of diameter three related to~$PSL_d(q)$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1339--1345},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a42/}
}
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A. A. Makhnev; L. Yu. Tsiovkina. Arc-transitive antipodal distance-regular graphs of diameter three related to~$PSL_d(q)$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1339-1345. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a42/