Genus distributions of orientable embeddings for two types of graphs.
Zeling Shao, Yanpei Liu · Australas. J Comb. · 2008
Abstract On the basis of the joint tree model introduced by Liu in 2003, the genus distributions of the orientable embeddings for further types of graphs can be obtained. These are apparently not easily obtained using overlap matrices, the formula of Jackson, etc. In this paper, however, by classifying the associated surfaces, we calculate the genus distributions of the orientable embeddings for two new types of graphs, namely, generalized necklaces and circulant necklaces. These are different from the graphs whose embedding distributions by genus have been obtained to date.