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, automorphism
The paper was received by the Editorial Office on May 21, 2018.
Alena Mukhamedovna Kagazezheva, Cand. Sci. (Phys.-Math.), Kabardino-Balkarian State University named after H. M. Berbekov, Nal’chik, 360004 Russia, e-mail: fkagazezhev@mail.ru
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