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Total Embedding Distributions of Circular Ladders

Authors


  • Contract grant sponsor: NNSFC; Contract grant number: 10901048 (to Y. C.); Contract grant sponsor: Hunan University Fund Project.

Abstract

The total embedding polynomial of a graph G is the bivariate polynomial

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where math formula is the number of embeddings, for math formula into the orientable surface math formula, and math formula is the number of embeddings, for math formula into the nonorientable surface math formula. The sequence math formula is called the total embedding distribution of the graph G; it is known for relatively few classes of graphs, compared to the genus distribution math formula. The circular ladder graph math formula is the Cartesian product math formula of the complete graph on two vertices and the cycle graph on n vertices. In this article, we derive a closed formula for the total embedding distribution of circular ladders.

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