Contract grant sponsor: NNSFC; Contract grant number: 10901048 (to Y. C.); Contract grant sponsor: Hunan University Fund Project.
Total Embedding Distributions of Circular Ladders
Article first published online: 9 AUG 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 74, Issue 1, pages 32–57, September 2013
How to Cite
Chen, Y., Gross, J. L. and Mansour, T. (2013), Total Embedding Distributions of Circular Ladders. J. Graph Theory, 74: 32–57. doi: 10.1002/jgt.21690
- Issue published online: 3 JUL 2013
- Article first published online: 9 AUG 2012
- Manuscript Revised: 25 MAY 2012
- Manuscript Received: 11 SEP 2011
- NNSFC. Grant Number: 10901048
- Hunan University
- graph embedding;
- total embedding distribution;
- circular ladders;
- overlap matrix;
- Chebyshev polynomials
The total embedding polynomial of a graph G is the bivariate polynomial
where is the number of embeddings, for into the orientable surface , and is the number of embeddings, for into the nonorientable surface . The sequence is called the total embedding distribution of the graph G; it is known for relatively few classes of graphs, compared to the genus distribution . The circular ladder graph is the Cartesian product 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.