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Enumerating Unlabelled Embeddings of Digraphs

  • Yichao Chen (a1), Xiaojian Gao (a2) and Yuanqiu Huang (a3)

A 2-cell embedding of an Eulerian digraph D into a closed surface is said to be directed if the boundary of each face is a directed closed walk in D. In this paper, a method is developed with the purpose of enumerating unlabelled embeddings for an Eulerian digraph. As an application, we obtain explicit formulas for the number of unlabelled embeddings of directed bouquets of cycles Bn , directed dipoles OD2n and for a class of regular tournaments T 2n+1.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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