TY - JOUR

T1 - On the Riemann-Hurwitz formula for regular graph coverings

AU - Mednykh, Alexander

N1 - Funding Information: 2020 Mathematics Subject Classification. Primary 30F40, 20H10; Secondary 14E20, 14H30. Key words and phrases. graph, semi-edge, invertible edge, branched covering, automorphism group, harmonic map. The author was supported by the Russian Science Foundation (grant 19-41-02005). Publisher Copyright: © 2022 American Mathematical Society.

PY - 2022

Y1 - 2022

N2 - The aim of this paper is to present a few versions of the Riemann-Hurwitz formula for a regular branched covering of graphs. By a graph, we mean a finite connected multigraph. The genus of a graph is defined as the rank of the first homology group. We consider a finite group acting on a graph, possibly with fixed and invertible edges, and the respective factor graph. Then, the obtained Riemann-Hurwitz formula relates genus of the graph with genus of the factor graph and orders of the vertex and edge stabilizers.

AB - The aim of this paper is to present a few versions of the Riemann-Hurwitz formula for a regular branched covering of graphs. By a graph, we mean a finite connected multigraph. The genus of a graph is defined as the rank of the first homology group. We consider a finite group acting on a graph, possibly with fixed and invertible edges, and the respective factor graph. Then, the obtained Riemann-Hurwitz formula relates genus of the graph with genus of the factor graph and orders of the vertex and edge stabilizers.

KW - Automorphism group

KW - Branched covering

KW - Graph

KW - Harmonic map

KW - Invertible edge

KW - Semi-edge

UR - http://www.scopus.com/inward/record.url?scp=85129418226&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e314dd8d-4821-3362-9469-1227b06c5e04/

U2 - 10.1090/conm/776/15618

DO - 10.1090/conm/776/15618

M3 - Article

AN - SCOPUS:85129418226

VL - 776

SP - 301

EP - 309

JO - Contemporary Mathematics

JF - Contemporary Mathematics

SN - 0271-4132

M1 - 14

ER -