Geodesic
On the Automorphism Group of an Antipodal Tight Graph of Diameter~$4$ with Parameters $(5,7,r)$
Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 123-135

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It is proved that the automorphism group of every $\mathrm{AT}4(5,7,r)$-graph acts intransitively on the set of its arcs. Moreover, it is established that the automorphism group of any strongly regular graph with parameters $(329,40,3,5)$ acts intransitively on the set of its vertices.
Keywords: distance-regular graph, antipodal tight graph, vertex-transitive graph. 
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     author = {L. Yu. Tsiovkina},
     title = {On the {Automorphism} {Group} of an {Antipodal} {Tight} {Graph} of {Diameter~}$4$ with {Parameters} $(5,7,r)$},
     journal = {Matemati\v{c}eskie zametki},
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     number = {1},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_1_a10/}
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L. Yu. Tsiovkina. On the Automorphism Group of an Antipodal Tight Graph of Diameter~$4$ with Parameters $(5,7,r)$. Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 123-135. http://geodesic.mathdoc.fr/item/MZM_2019_105_1_a10/