Some Results On The Embeddability Of Graphs

The embedding and genera of a graph is an important subject in topological graph theory. In this paper, firstly, we give the formulae of the genus of 3-regular graph; Secondly, we prove that two classes of graphs are up-embedable; Thirdly, we investigate the properties of sub-edge-set's deficiency ; Lastly, we give the relations between the STP number of a graph and the embedability of a graph . Some results will be given in the thesis as follows:1. Giving a formulae of computing maximum genus of a 3-regular graph and extend it to the general condition;2. Giving the upper-embeddability of special bipartite graphs;3. Giving the relations between the maximum genus of a graph and its independent edges and obtaining the graph is upper-embeddability if it is a plane graph and whose dual graph has 1-factors;4. Giving the interpolation theorem on the sub-edge-set's deficiency according to the formulae of Betti deficiency given by Nebesky.5.Giving the relations between the STP number and the embeddablity of a graph.