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 language | English |
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Pages (from-to) | 595-606 |
Number of pages | 12 |
Journal | Acta Mathematica Sinica, English Series |
Volume | 27 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2011 |
Keywords
- Embedding
- genus
- genus distribution
- genus polynomial