1. Genus polynomials of cycles with double edges.
- Author
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Baek, Eunyoung and Park, Jongyook
- Subjects
- *
POLYNOMIALS , *HOMEOMORPHISMS , *GRAPHIC methods , *EQUIVALENCE classes (Set theory) , *EMBEDDINGS (Mathematics) , *VERTEX operator algebras , *MATHEMATICS - Abstract
Two 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 a is the number of equivalence classes of embeddings of G into the orientable surface S 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. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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