Geodesic
On automorphism groups of AT4(7, 9,r)-graphs and their local subgraphs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 263-271

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The paper is devoted to the problem of classification of AT4$(p,p+2,r)$-graphs. An example of an AT4$(p,p+2,r)$-graph with $p=2$ is provided by the Soicher graph with intersection array $\{56, 45, 16,1;1,8, 45, 56\}$. The question of existence of AT4$(p,p+2,r)$-graphs with $p>2$ is still open. One task in their classification is to describe such graphs of small valency. We investigate the automorphism groups of a hypothetical AT4$(7,9,r)$-graph and of its local graphs. The local graphs of each AT4$(7,9,r)$-graph are strongly regular with parameters $(711,70,5,7)$. It is unknown whether a strongly regular graph with these parameters exists. We show that the automorphism group of each AT4$(7,9,r)$-graph acts intransitively on its arcs. Moreover, we prove that the automorphism group of each strongly regular graph with parameters $(711,70,5,7)$ acts intransitively on its vertices.
Keywords: antipodal tight graph, strongly regular graph
Mots-clés : automorphism. 
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     author = {L. Yu. Tsiovkina},
     title = {On automorphism groups of {AT4(7,} 9,r)-graphs and their local subgraphs},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {263--271},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a22/}
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L. Yu. Tsiovkina. On automorphism groups of AT4(7, 9,r)-graphs and their local subgraphs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 263-271. http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a22/