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On the Riemann-Hurwitz formula for graph coverings

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 stabilisers.

preprint2015arXivOpen access
A. D. Mednykh
math.ATmath.COmath.CV
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A. D. Mednykh

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