| 摘要 | 第1-7页 |
| Abstract | 第7-12页 |
| 1 Introduction | 第12-24页 |
| ·Background and some results on graph energy | 第12-15页 |
| ·Background on hypoenergetic graphs | 第15-19页 |
| ·Our main results | 第19-24页 |
| 2 All connected graphs with maximum degree at most 3 whose energies less than or equal to the number of vertices | 第24-46页 |
| ·Preliminaries | 第24-25页 |
| ·The cases for tree, unicyclic and bicyclic graphs | 第25-37页 |
| ·Proof of Theorem 1.12 | 第37-46页 |
| 3 Hypoenergetic and strongly hypoenergetic k-cyclic graphs with maximum degree at least 4 | 第46-62页 |
| ·Hypoenergetic and strongly hypoenergetic trees | 第46-51页 |
| ·Hypoenergetic and strongly hypoenergetic k-cyclic graphs with maximum degree at least 4 | 第51-56页 |
| ·Hypoenergetic unicyclic graphs with maximum degree at least 4 | 第56-57页 |
| ·Hypoenergetic bicyclic graphs with maximum degree at least 4 | 第57-59页 |
| ·Hypoenergetic tricyclic graphs with maximum degree at least 4 | 第59-62页 |
| 4 On non-hypoenergetic triregular graphs | 第62-74页 |
| ·Preliminaries | 第62-63页 |
| ·Triregular trees | 第63-66页 |
| ·Triregular unicyclic graphs | 第66-69页 |
| ·Triregular bicyclic graphs | 第69-74页 |
| Bibliography | 第74-80页 |
| Acknowledgement | 第80-82页 |
| Resume | 第82页 |
