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On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups

  • Giovanni Moreno EMAIL logo and Monika Ewa Stypa
Published/Copyright: August 17, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 3

Abstract

We prove that the Cayley graph and the coset geometry of the von Dyck group D(a, b, c) are linked by a vertex-to-edge duality.

MSC 2010: Primary 05E18; 20F65; 05C25; 05C15; 52C20; 51E99; 20F05; 22E40
Keywords: group actions on combinatorial structures; geometric group theory; incidence geometry; graphs and abstract algebra; tilings in 2 dimensions

The first author was supported by the project P201/12/G028 of the Czech Republic Grant Agency (GA ČR).

The second author was supported by the doctoral school of the University of Salerno.

(Communicated by Július Korbaš)

acknowledgement

The authors would like to thank P. Longobardi and C. Sica for their helpful suggestions, and also the referees for carefully reading the manuscript.

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Received: 2013-7-12
Accepted: 2013-10-23
Published Online: 2016-8-17
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0154
Keywords for this article
group actions on combinatorial structures; geometric group theory; incidence geometry; graphs and abstract algebra; tilings in 2 dimensions

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  5. Research Article
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  9. Research Article
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  11. Research Article
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