I. INTRODUCTION  
II. PRELIMINARY  
A. Graph  
B. Graph Neural Network  
C. Large Language Models  
D. Graph Description Language  
III. GRAPH STRUCTURE UNDERSTANDING TASKS  
A. Task Introduction  
B. Graph Structure Understanding Methods  
C. Comparisons and Discussions  
IV. GRAPH LEARNING TASKS  
A. Tasks Introduction  
B. Graph Learning Methods  
C. Comparisons and Discussions  
V. GRAPH-FORMED REASONING  
A. Tasks Introduction  
B. Graph-formed Reasoning Methods  
C. Comparisons and Discussions  
VI. GRAPH REPRESENTATION  
A. Tasks Introduction  
B. Graph Representation Methods  
C. Comparisons and Discussions  
VII. KNOWLEDGE GRAPH BASED AUGMENTED RETRIEVAL  
A. LLMs limitations and comparison with KGs  
B. Solutions to LLMs limitations  
C. Other KG + LLMs works  
D. Summary  
VIII. GRAPH-LLM BASED APPLICATIONS  
IX. BENCHMARK DATASETS AND EVALUATIONS  
A. Datasets  
B. Evaluations  
X. FUTURE DIRECTIONS  
A. More Complex Graph Problems  
E. Better Graph Prompts  
C. Better LLM-GNN Pipelines  
D. Graph Foundation Model  
F. Modal Alignment  
G. Explainability  
H. Efficiency on Large-scale Graphs  
XI. CONCLUSIONS