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

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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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     author = {M. M. Isakova and A. A. Makhnev and Mingzhu Chen},
     title = {On automorphisms of a graph with an intersection array $\{44,30,9;1,5,36\}$},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {47--55},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2024_26_3_a3/}
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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/