Total embedding distributions of circular ladders

Yichao Chen, Jonathan L. Gross, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


The total embedding polynomial of a graph G is the bivariate polynomial IG(x,y)=Σi=0∞aixi+Σj=1∞bjyj,where ai is the number of embeddings, for i=0,1,., into the orientable surface Si, and bj is the number of embeddings, for j=1,2,., into the nonorientable surface Nj. The sequence {ai(G)|i≥0} {bj(G)|j≥1} is called the total embedding distribution of the graph G; it is known for relatively few classes of graphs, compared to the genus distribution {ai(G)|i≥0}. The circular ladder graph CLn is the Cartesian product K2□Cn 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.

Original languageEnglish
Pages (from-to)32-57
Number of pages26
JournalJournal of Graph Theory
Issue number1
StatePublished - Sep 2013


  • Chebyshev polynomials
  • circular ladders
  • graph embedding
  • overlap matrix
  • total embedding distribution

ASJC Scopus subject areas

  • Geometry and Topology


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