Genus polynomials of cycles with double edges

Eunyoung Baek, Jongyook Park

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Two cellular embeddings i: GTwo cellular embeddings i: G → S and j: G → S of a connected graph G into a closed orientable surface S are equivalent if there is an orientation-preserving surface homeomorphism h: S → S such that hi = j. The genus polynomial of a graph G is defined by, where ag is the number of equivalence classes of embeddings of G into the orientable surface Sg with g genera. In this paper, we compute the genus polynomial of a graph obtained from a cycle by replacing each edge by two multiple edges.

Original languageEnglish
Pages (from-to)595-606
Number of pages12
JournalActa Mathematica Sinica, English Series
Volume27
Issue number3
DOIs
StatePublished - Mar 2011

Keywords

  • Embedding
  • genus
  • genus distribution
  • genus polynomial

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