Regular and orientably-regular maps with quasiprimitive automorphism groups on vertices

Jajcay，Robert1; Li，Cai Heng2; Širáň，Jozef3; Wang，Yan4

2019-12-01

10.1007/s10711-019-00440-6

GEOMETRIAE DEDICATA   影响因子和分区

0046-5755

1572-9168

Regular and orientably-regular maps are central to the part of topological graph theory concerned with highly symmetric graph embeddings. Classification of such maps often relies on factoring out a normal subgroup of automorphisms acting intransitively on the set of the vertices of the map. Maps whose automorphism groups act quasiprimitively on their vertices do not allow for such factorization. Instead, we rely on classification of quasiprimitive group actions which divides such actions into eight types, and we show that four of these types, HS, HC, SD, and CD, do not occur as the automorphism groups of regular or orientably-regular maps. We classify regular and orientably-regular maps with automorphism groups of the HA type, and construct new families of regular as well as both chiral and reflexible orientably-regular maps with automorphism groups of the TW and PA types. We provide a brief summary of the known results concerning the AS type, which has been extensively studied before.

Automorphism group Orientably-regular map Quasiprimitive group action Regular map

SCI

英语

其他

[VEGA 1/0719/18]

Mathematics

Mathematics

WOS:000494223800020

SPRINGER

MATHEMATICS

2-s2.0-85063203253

Scopus

1.Comenius University,Bratislava,Slovakia
2.Department of MathematicsSouthern University of Science and Technology,Shenzhen,518055,China
3.Slovak University of Technology,Bratislava,Slovakia
4.Yan Tai University,Yantai,China

Jajcay，Robert,Li，Cai Heng,Širáň，Jozef,et al. Regular and orientably-regular maps with quasiprimitive automorphism groups on vertices[J]. GEOMETRIAE DEDICATA,2019,203(1):389-418.

Jajcay，Robert,Li，Cai Heng,Širáň，Jozef,&Wang，Yan.(2019).Regular and orientably-regular maps with quasiprimitive automorphism groups on vertices.GEOMETRIAE DEDICATA,203(1),389-418.

Jajcay，Robert,et al."Regular and orientably-regular maps with quasiprimitive automorphism groups on vertices".GEOMETRIAE DEDICATA 203.1(2019):389-418.