Two Moore's theorems for graphs

Mednykh, Alexander
•
Mednykh
•
Ilya
2020
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ISSN
0049-4704
DOI
e-ISSN
2464-8728
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.
Journal
Subjects
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
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Licence