Аннотация:
Distance-regular graph $\Gamma$ with intersection array $\{117, 80, 18, 1; 1, 18, 80, 117\}$ is an $AT4$-graph. Antipodal quotient $\bar \Gamma$ has parameters $(378, 117, 36, 36)$. Both graphs have strongly regular neighbourhoods with parameters $(117, 36, 15, 9)$. In the work automorphisms of the said graphs are found. In particular, there exist graphs of rank 3 with parameters $(117, 36, 15, 9)$ and $(378, 117, 36, 36)$, and graph with intersection array $\{117, 80, 18, 1; 1, 18, 80, 117\}$ is not arc-transitive.
Ключевые слова:strongly regular graph, eigenvalue, automorphism of graph.