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Three local actions in 6-valent arc-transitive graphsHujdurović, Ademir, 1987- ; Potočnik, Primož, 1971- ; Verret, GabrielIt is known that there are precisely three transitive permutation groups of degree ▫$6$▫ that admit an invariant partition with three parts of size ▫$2$▫ such that the kernel of the action on the ... parts has order ▫$4$▫; these groups are called ▫$A_4(6)$▫, ▫$S_4(6d)$▫ and ▫$S_4(6c)$▫. For each ▫$L\in \{A_4(6), S_4(6d), S_4(6c)\}$▫, we construct an infinite family of finite connected ▫$6$▫-valent graphs ▫$\{\Gamma_n\}_{n\in \mathbb{N}}$▫ and arc-transitive groups ▫$G_n \le \rm{Aut}(\Gamma_n)$▫ such that the permutation group induced by the action of the vertex-stabiliser ▫$(G_n)_v$▫ on the neighbourhood of a vertex ▫$v$▫ is permutation isomorphic to ▫$L$▫, and such that ▫$|(G_n)_v|$▫ is exponential in ▫$|\rm{V}(\Gamma_n)|$▫. These three groups were the only transitive permutation groups of degree at most ▫$7$▫ for which the existence of such a family was undecided. In the process, we construct an infinite family of cubic ▫$2$▫-arc-transitive graphs such that the dimension of the ▫$1$▫-eigenspace over the field of order ▫$2$▫ of the adjacency matrix of the graph grows linearly with the order of the graph.Source: Journal of graph theory. - ISSN 0364-9024 (Vol. 99, iss. 2, Feb. 2022, str. 207-216)Type of material - article, component part ; adult, seriousPublish date - 2022Language - englishCOBISS.SI-ID - 74263555
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Hujdurović, Ademir, 1987- | 32518 |
Potočnik, Primož, 1971- | 18838 |
Verret, Gabriel | 28586 |
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