Two Moore’s Theorems for Graphs Full article
| Journal |
Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
ISSN: 0049-4704 |
||||
|---|---|---|---|---|---|
| Output data | Year: 2020, Volume: 52, Pages: 469-476 Pages count : 8 DOI: 10.13137/2464-8728/30918 | ||||
| Tags | automorphism group; graph; harmonic action; orbifold | ||||
| Authors |
|
||||
| Affiliations |
|
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 invert-ible edges. Define 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 automor-phisms acting on a Riemann surface of genus g. In the present paper, we investigate cyclic group (Formula presented)nacting purely harmonically on a graph X of genus g with fixed points. Given subgroup (Formula presented)d< (Formula presented)n, we find the signature of orbifold X/(Formula presented)dthrough the signature of orbifold X/(Formula presented)n. As a result, we obtain formulas for the number of fixed points for generators of group (Formula presented)dand for genus of orbifold X/(Formula presented)d. For Riemann surfaces, similar results were obtained earlier by M. J. Moore. © 2020. All Rights Reserved.
Cite:
Mednykh A.
, Mednykh I.
Two Moore’s Theorems for Graphs
Rendiconti dell'Istituto di Matematica dell'Universita di Trieste. 2020. V.52. P.469-476. DOI: 10.13137/2464-8728/30918 Scopus OpenAlex
Two Moore’s Theorems for Graphs
Rendiconti dell'Istituto di Matematica dell'Universita di Trieste. 2020. V.52. P.469-476. DOI: 10.13137/2464-8728/30918 Scopus OpenAlex
Identifiers:
| Scopus: | 2-s2.0-85108854523 |
| OpenAlex: | W3200402322 |