Geodesic
On a vertex-symmetric graph with intersection array 205, 136, 1; 1, 68, 205
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 91-97 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. Makhnev and D. Paduchikh found intersection arrays of distance-regular graphs that are locally strongly regular with the second eigenvalue 3. A. Makhnev and M. Samoilenko added to this list the intersection arrays {196, 76, 1; 1, 19, 196} and {205, 136, 1; 1, 68, 205}. However, graphs with these intersection arrays cannot be locally strongly regular. The existence of graphs with these intersection arrays is unknown. We find possible orders and fixed-point subgraphs for the elements of the automorphism group of a distance-regular graph with intersection array {205, 136, 1; 1, 68, 205}. It is proved that a vertex-transitive distance-regular graph with this intersection array is a Cayley graph.
Keywords: distance-regular graph
Mots-clés : automorphism. 
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A. M. Kagazezheva. On a vertex-symmetric graph with intersection array 205, 136, 1; 1, 68, 205. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 91-97. http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a9/

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