petrie duality and the anstee–robertson graph
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ID: 211729
2015
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Abstract
We define the operation of Petrie duality for maps, describing its general properties both geometrically and algebraically. We give a number of examples and applications, including the construction of a pair of regular maps, one orientable of genus 17, the other non-orientable of genus 52, which embed the 40-vertex cage of valency 6 and girth 5 discovered independently by Robertson and Anstee. We prove that this map (discovered by Evans) and its Petrie dual are the only regular embeddings of this graph, together with a similar result for a graph of order 40, valency 6 and girth 3 with the same automorphism group.
| Reference Key |
jones2015symmetrypetrie
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|---|---|
| Authors | ;Gareth A. Jones;Matan Ziv-Av |
| Journal | journal of hospitality and tourism management |
| Year | 2015 |
| DOI |
10.3390/sym7042206
|
| URL | |
| Keywords | Keywords not found |
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