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Archdeacon, Dan; Conder, Marston and Siran, Jozef
(2014).
DOI: https://doi.org/10.1090/S0002-9947-2013-06079-5
Abstract
A cellular embedding of a connected graph (also known as a map) on an orientable surface has trinity symmetry if it is isomorphic to both its dual and its Petrie dual. A map is regular if for any two incident vertex-edge pairs there is an automorphism of the map sending the first pair onto the second. Given a map M with all vertices of the same degree d, for any e relatively prime to d the power map Me is formed from M by replacing the cyclic rotation of edges at each vertex on the surface with the e th power of the rotation. A map is kaleidoscopic if all of its power maps are pairwise isomorphic. In this paper, we present a covering construction that gives infinite families of kaleidoscopic regular maps with trinity symmetry.
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About
- Item ORO ID
- 37407
- Item Type
- Journal Item
- ISSN
- 1088-6850
- 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
- © 2013 American Mathematical Society
- Related URLs
- Depositing User
- Jozef Širáň