Three local actions in 6-valent arc-transitive graphs

Ademir Hujdurović (Avtor), Primož Potočnik (Avtor), Gabriel Verret (Avtor)

Povzetek

It 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.

Ključne besede

lastni podprostor za lastno vrednost 1;ločno-tranzitiven graf;grupa avtomorfizmov;one-eigenspace;arc-transitive graph;automorphism group;

Podatki

Jezik:	Angleški jezik
Leto izida:	2022
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	519.17
COBISS:	74263555
ISSN:	0364-9024
Št. ogledov:	822
Št. prenosov:	101
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarne ključne besede:	lastni podprostor za lastno vrednost 1;ločno-tranzitiven graf;grupa avtomorfizmov;
Strani:	str. 207-216
Letnik:	ǂVol. ǂ99
Zvezek:	ǂiss. ǂ2
Čas izdaje:	Feb. 2022
DOI:	10.1002/jgt.22735
ID:	13555633