Geodesic
On automorphisms of a distance-regular graph with intersection array 69,56,10;1,14,60
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 3, pp. 182-190
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Let $\Gamma$ be a distance-regular graph of diameter 3 with eigenvalues $\theta_0>\theta_1>\theta_2>\theta_3$. If $\theta_2=-1$, then the graph $\Gamma_3$ is strongly regular and the complementary graph $\bar\Gamma_3$ is pseudogeometric for $pG_{c_3}(k,b_1/c_2)$. If $\Gamma_3$ does not contain triangles and the number of its vertices $v$ is less than 800, then $\Gamma$ has intersection array $\{69,56,10;1,14,60\}$. In this case $\Gamma_3$ is a graph with parameters (392,46,0,6) and $\bar \Gamma_2$ is a strongly regular graph with parameters (392,115,18,40). Note that the neighborhood of any vertex in a graph with parameters $(392,115,18,40)$ is a strongly regular graph with parameters $(115,18,1,3)$, and its existence is unknown. In this paper, we find possible automorphisms of this strongly regular graph and automorphisms of a distance-regular graph with intersection array $\{69,56,10;1,14,60\}$. In particular, it is proved that the latter graph is not arc-transitive.
Keywords: distance-regular graph, automorphism of a graph. 
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A. A. Makhnev; M. S. Nirova. On automorphisms of a distance-regular graph with intersection array 69,56,10;1,14,60. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 3, pp. 182-190. http://geodesic.mathdoc.fr/item/TIMM_2017_23_3_a15/

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