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On discrete versions of two Accola’s theorems about automorphism groups of Riemann surfaces. (English) Zbl 1379.31015

Summary: In this paper we give a few discrete versions of Robert Accola’s results on Riemann surfaces with automorphism groups admitting partitions. As a consequence, we establish a condition for \(\gamma \)-hyperelliptic involution on a graph to be unique. Also we construct an infinite family of graphs with more than one \(\gamma \)-hyperelliptic involution.

MSC:

31C20 Discrete potential theory
05C10 Planar graphs; geometric and topological aspects of graph theory
57M12 Low-dimensional topology of special (e.g., branched) coverings
30F10 Compact Riemann surfaces and uniformization
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