研究期間：10108~10207;The purpose of this project has three parts. In the first part, we study graph nullity problems and minimum rank problems. We focus on the following problems: 1. Give a complete characterization of graphs having rank 5. 2. Give a complete characterization of bipartite graphs having rank 6. 3. Study singular graphs. 4. Study η(L(T)), where L(T) is the line graph of tree T. 5. Study minimum rank and zero forcing number for Hamming graphs. 6. Study Delta Conjecture and Graph Complement Conjecture. 7. Study minimum rank of full patterns and its applications in communication complexity. In the second part, we study diffusion problem on social network. In the third part of the project, we deal with circular chromatic number and study Dichotomy Conjecture for Digraph Homomorphism and Dichotomy Conjecture for CSP
