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Jajcay, Robert; Li, Cai-Heng; Širáň, Jozef and Wang, Yan
(2019).
DOI: https://doi.org/10.1007/s10711-019-00440-6
Abstract
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.
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About
- Item ORO ID
- 60701
- Item Type
- Journal Item
- ISSN
- 0046-5755
- Project Funding Details
-
Funded Project Name Project ID Funding Body Not Set APVV 0136/12 Not Set Not Set APVV-15-0220 Not Set Not Set VEGA 1/0026/16 Not Set Not Set VEGA 1/0142/17 Not Set Not Set NSFC 11371307 Not Set - Keywords
- Regular map; Orientably-regular map; Automorphism group; Quasiprimitive group action
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2019 Springer Nature B.V.
- Depositing User
- Jozef Širáň