Minimum genera of certain types of graphs

Abstract

In 2003, Liu set up the joint tree model such that an embedding of a graph on a surface can be represented by a joint tree, further by an associated surface of it. Divide the associated surface into segments layer by layer and do some operations on the layer division to obtain the associated surface of minimum genus. Based on it, in this paper, we obtain the genera of two new types of graphs. Additionally, the genera of several graphs are determined as applications.