Geodesic
Automorphisms of distance-regular graph with intersection array $\{24,18,9;1,1,16\}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1547-1552

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Koolen and Park classified Shilla graphs with $b=2$ and with $b=3$. Prime divisors of orders of automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a hypothetical distance-regular graph $\Gamma$ with intersection array $\{24,18,9;1,1,16\}$. Let $G={\rm Aut}(\Gamma)$ is nonsolvable group, $\bar G=G/S(G)$ and $\bar T$ is the socle of $\bar G$. Then $G$ contains now elements of order 35 and $\bar T\cong J_2, A_{10}$ or $\Omega^+_8(2)$. In particular graph $\Gamma$ is not vertex symmetric.
Keywords: distance-regular graph
Mots-clés : automorphism. 
@article{SEMR_2019_16_a73,
     author = {A. A. Makhnev},
     title = {Automorphisms of distance-regular graph with intersection array $\{24,18,9;1,1,16\}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1547--1552},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a73/}
}
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A. A. Makhnev. Automorphisms of distance-regular graph with intersection array $\{24,18,9;1,1,16\}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1547-1552. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a73/