Complete regular dessins of odd prime power order

摘要

A dessin is a 2-cell embedding of a connected 2-coloured bipartite graph into an orientable closed surface. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts regularly on the edges. In this paper we employ group-theoretic method to determine and enumerate the isomorphism classes of regular dessins with complete bipartite underlying graphs of odd prime power order. (C) 2018 Elsevier B.V. All rights reserved.