Options
Two Moore's theorems for graphs
Mednykh, Alexander
Mednykh
Ilya
2020
Loading...
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.
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