| Abstract (In Chinese) | 第1-9页 |
| Abstract (In English) | 第9-13页 |
| Preliminaries | 第13-17页 |
| Chapter 1. Average genus of graphs with forbidden structures | 第17-36页 |
| ·Introduction | 第17-19页 |
| ·Lower bound for the maximum genus of a graph | 第19-24页 |
| ·The technique of vertex-splitting for a graph | 第24-27页 |
| ·Lower bounds for the average genus of a graph | 第27-32页 |
| ·Limit points for the average genus | 第32-36页 |
| Chapter 2. Structure for a graph with average genus | 第36-46页 |
| ·Introduction | 第36-39页 |
| ·The structure for a graph with average genus equal to its subgraph | 第39-41页 |
| ·The structure for a 3-regular graph with γ_(avg)(G)=(1/2)γ_M(G) | 第41-46页 |
| Chapter 3. The average crosscap number of two classes of graphs | 第46-59页 |
| ·Definition | 第46-47页 |
| ·The average crosscap number for bar-amalgamation | 第47-49页 |
| ·The average crosscap number of a cactus | 第49-51页 |
| ·The average crosscap number of graphs with maximum genus 1 | 第51-57页 |
| ·Asymptotics | 第57-59页 |
| Chapter 4. Structure for graphs with average crosscap number | 第59-80页 |
| ·Priliminaries | 第59-60页 |
| ·The distribution of average crosscap number | 第60-62页 |
| ·2-edge connected graph with small average crosscap number | 第62-75页 |
| ·1-edge connected graph with small average crosscap number | 第75-77页 |
| ·Share values of average crosscap number | 第77-80页 |
| Chapter 5. Bounds for the average crosscap number | 第80-89页 |
| ·Introduction | 第80-81页 |
| ·Some basic results | 第81-84页 |
| ·Main results | 第84-89页 |
| Chapter 6. Some problems for further researched | 第89-92页 |
| Bibliography | 第92-94页 |
| 博士研究生期间所发表和接收的一些工作 | 第94页 |
