Geodesic
On automorphisms of a graph with an intersection array $\{44,30,9;1,5,36\}$
Vladikavkazskij matematičeskij žurnal, Tome 26 (2024) no. 3, pp. 47-55 
M. M. Isakova; A. A. Makhnev; Mingzhu Chen. On automorphisms of a graph with an intersection array $\{44,30,9;1,5,36\}$. Vladikavkazskij matematičeskij žurnal, Tome 26 (2024) no. 3, pp. 47-55. http://geodesic.mathdoc.fr/item/VMJ_2024_26_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the set $X$ automorphisms of the graph $\Gamma$ let ${\rm Fix}(X)$ be a set of all vertices of $\Gamma$ fixed by any automorphism from $X$. There are $7$ feasible intersection arrays of distance regular graphs with diameter $3$ and degree $44$. Early it was proved that for fifth of them graphs do not exist. In this paper it is founded possible automorphisms of distance regular graph with intersection array $\{44,30,9;1,5,36\}$. The proof of the theorem is based on Higman’s method of working with automorphisms of a distance regular graph. The consequence of the main result is is the following: Let $\Gamma$ be a distance regular graph with intersection array $\{44,30,9;1,5,36\}$ and the group $G={\rm Aut}(\Gamma)$ acts vertex-transitively; then $G$ acts intransitively on the set arcs of $\Gamma$.

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[2] Chen Mingzhu, Makhnev, A. A. and Klimov, V. S., “On Distance Regular Graphs of Diameter $3$ and Degrees $44$”, Youth Conference of the Institute of Mechanics and Mathematics. Ural Branch of the Russian Academy of Sciences, Abstracts of Reports (Ekaterinburg, 2024), 1132–1134 (in Russian)

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