Genus Distributions for Several Types of Ladder-class Graphs

Calculating the genus distributions of ladder graphs is a concerned topic in topological graph theory. In this paper, we formulate several ladder-class graphs by using a starting graph iterative amalgamation with copies of a path to construct a base graph and then adding some edges to the appointed root-vertices of the base graph. By means of transfer matrix and a finer partition of the embeddings, the explicit formulas for the genus distribution polynomials of four types of ladder-class graphs are derived.