Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/30918
Title: Two Moore's theorems for graphs
Authors: Mednykh, Alexander
Mednykh
Ilya
Keywords: graphautomorphism groupharmonic actionorbifold
Issue Date: 2020
Publisher: EUT Edizioni Università di Trieste
Source: Alexander Mednykh and Ilya Mednykh, "Two Moore's theorems for graphs" in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)", EUT Edizioni Università di Trieste, Trieste, 2020
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Abstract: 
Let X be a finite connected graph, possibly with loops and multiple edges. An automorphism group of X acts purely harmonically if it acts freely on the set of directed edges of X and has no invertible edges. Dene a genus g of the graph X to be the rank of the first homology group. A finite group acting purely harmonically on a graph of genus g is a natural discrete analogue of a finite group of automorphisms acting on a Riemann surface of genus g: In the present paper, we investigate cyclic group Zn acting purely harmonically on a graph X of genus g with fixed points. Given subgroup Zd < Zn; we find the signature of orbifold X=Zd through the signature of orbifold X=Zn: As a result, we obtain formulas for the number of fixed points for generators of group Zd and for genus of orbifold X=Zd: For Riemann surfaces, similar results were obtained earlier by M. J. Moore.
Type: Article
URI: http://hdl.handle.net/10077/30918
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/30918
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), 1st and 2nd Issue

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