| Abstract | 第6-7页 |
| Chinese Abstract | 第8-10页 |
| Acknowledgements | 第10-20页 |
| List of Abbreviations | 第20-22页 |
| Chapter 1 Introduction and Overview | 第22-30页 |
| 1.1 A literature review | 第23-25页 |
| 1.1.1 Domination Polynomial | 第23页 |
| 1.1.2 Independent Domination Polynomial | 第23-24页 |
| 1.1.3 Total Domination Polynomial | 第24页 |
| 1.1.4 Topological Indices | 第24-25页 |
| 1.2 The Definition of a Graph | 第25-28页 |
| 1.3 Thesis Outline | 第28-30页 |
| Chapter 2 Domination Polynomial of Some Special Graphs | 第30-47页 |
| 2.1 Introduction | 第31-32页 |
| 2.2 Properties of Domination Polynomial and Its Coefficients | 第32-37页 |
| 2.3 Domination Polynomial of Some Special Graphs | 第37-42页 |
| 2.3.1 Domination Polynomial of Complete Graph Kn | 第37页 |
| 2.3.2 Domination Polynomial of Path Pn | 第37-40页 |
| 2.3.3 Domination Polynomial of Cycle Cn | 第40-42页 |
| 2.4 Recurrence Relation | 第42-47页 |
| Chapter 3 Independent Domination Polynomial of Some Special Graphs | 第47-57页 |
| 3.1 Introduction | 第48-49页 |
| 3.2 Bounds on The Independent Domination Number | 第49-51页 |
| 3.2.1 General Bounds | 第49-50页 |
| 3.2.2 Domination And Independence | 第50-51页 |
| 3.3 The Independent Domination Polynomial | 第51-53页 |
| 3.4 Independent Domination Polynomial of Some Special Graphs | 第53-56页 |
| 3.4.1 Independent Domination Polynomial of Complete GraphKn | 第53页 |
| 3.4.2 Independent domination polynomial of complete bipar-tite graph K_(m,n) | 第53页 |
| 3.4.3 Independent Domination Polynomial of Bi-star GraphB(m, n) | 第53页 |
| 3.4.4 Independent Domination Polynomial of Star Graph K_(1,m) | 第53-54页 |
| 3.4.5 Independent domination polynomial of friendship graph F_m | 第54页 |
| 3.4.6 Independent Domination Polynomial of The Path P_n | 第54-55页 |
| 3.4.7 Independent Domination Polynomial of The Cycle C_n | 第55页 |
| 3.4.8 Independent Domination Polynomial of Other Graphs | 第55-56页 |
| 3.5 Recurrence Equations | 第56-57页 |
| Chapter 4 Total Domination Polynomial of Some Special Graphs | 第57-74页 |
| 4.1 Introduction | 第58-60页 |
| 4.2 Properties of Total Domination Polynomial | 第60-65页 |
| 4.3 Total Domination Polynomial of Some Special Graphs | 第65-71页 |
| 4.3.1 Total Domination Polynomial of G○K_1 | 第65页 |
| 4.3.2 Total Domination Polynomial of Complete Graph K_n | 第65页 |
| 4.3.3 Total Domination Polynomial of Complete Bipartite GraphK_(r,s) | 第65-66页 |
| 4.3.4 Total Domination Polynomial of Tree T_n | 第66页 |
| 4.3.5 Total Domination Polynomial of The Path P_n | 第66-67页 |
| 4.3.6 Total Domination Polynomial of The Cycle C_n | 第67-70页 |
| 4.3.7 Total Domination Polynomial of Other Graph classes | 第70-71页 |
| 4.4 Reduction-Formulas of Total Domination Polynomials | 第71-72页 |
| 4.5 Recurrence Equations | 第72-74页 |
| Chapter 5 Topological Indices of Some Special Graphs | 第74-84页 |
| 5.1 Introduction | 第75-76页 |
| 5.2 Topological Indices | 第76-80页 |
| 5.3 Topological Indices of Some Special Graphs | 第80-84页 |
| 5.3.1 Nano Tubes VC_5C_7[p, q],(p, q>1) | 第80-82页 |
| 5.3.2 Some Nano-structures | 第82页 |
| 5.3.3 Tadpole Graph T_(n,k) | 第82页 |
| 5.3.4 Wheel Graph W_n | 第82-84页 |
| Chapter 6 Results and Discussion | 第84-117页 |
| 6.1 Research Methodology | 第85-90页 |
| 6.1.1 The Cyclic silicates graphs | 第85-86页 |
| 6.1.2 The special graph G_n | 第86-87页 |
| 6.1.3 The Cayley Tree Γ~k | 第87-88页 |
| 6.1.4 The Square Lattice Graph SL_n | 第88-89页 |
| 6.1.5 The Complete Bipartite Graph K_(m,n) | 第89-90页 |
| 6.2 The Three Polynomials | 第90-99页 |
| 6.3 Topological Indices | 第99-117页 |
| Chapter 7 General Conclusion and Open Problems | 第117-120页 |
| 7.1 Conclusion | 第118页 |
| 7.2 Open Problems | 第118-120页 |
| References | 第120-129页 |
| List of Publications | 第129页 |
