On automorphisms of a graph with an intersection array {44,30,9;1,5,36}

Автор: Isakova M.M., Makhnev A.A., Mingzhu Ch.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.26, 2024 года.

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For the set X automorphisms of the graph Γ let Fix(X) be a set of all vertices of Γ 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 Γ be a distance regular graph with intersection array {44,30,9;1,5,36} and the group G=Aut(Γ) acts vertex-transitively; then G acts intransitively on the set arcs of Γ.

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Strongly regular graph, fixed point subgraph, distance regular graph, automorphism

Короткий адрес: https://sciup.org/143183059

IDR: 143183059   |   DOI: 10.46698/x0578-3097-1488-l

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