Total Embedding Distributions of Circular Ladders

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 non-orientable 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 K22Cn of the complete graph on two vertices and the cycle graph on n vertices. In this paper, we derive a closed formula for the total embedding distribution of circular ladders.