Graph Theory

  1. Applications of Graph Theory
    1. Computer Science
      1. Data Structures
        1. Graph Data Structures
          1. Adjacency List
            1. Adjacency Matrix
              1. Incidence List
              2. Tree Data Structures
                1. Binary Trees
                  1. AVL Trees
                    1. Red-Black Trees
                  2. Network Topologies
                    1. LAN/WAN Design
                      1. Internet Connectivity Models
                        1. Network Reliability and Resilience
                        2. Compiler Design
                          1. Control Flow Graphs
                            1. Optimizing Code with Data Flow Analysis
                              1. Register Allocation
                              2. Database Schemas
                                1. Entity-Relationship Modeling
                                  1. Query Optimization
                                2. Biology
                                  1. Phylogenetic Trees
                                    1. Evolutionary Relationships
                                      1. Species Classification
                                        1. Algorithmic Reconstruction
                                        2. Protein-Protein Interaction Networks
                                          1. Biological Pathways
                                            1. Functional Modules
                                              1. Drug Discovery
                                            2. Social Sciences
                                              1. Social Network Analysis
                                                1. Community Detection
                                                  1. Influence and Reach
                                                    1. Sociograms
                                                    2. Small-World Network Models
                                                      1. Characteristics of Social Networks
                                                        1. Information Spread and Viral Marketing
                                                      2. Transportation and Logistics
                                                        1. Traffic Flow Optimization
                                                          1. Congestion Analysis
                                                            1. Signal Timing
                                                            2. Route Planning
                                                              1. Shortest Path Algorithms
                                                                1. Vechical Routing Problems
                                                                  1. Public Transportation Design
                                                                2. Telecommunications
                                                                  1. Design and Analysis of Communication Networks
                                                                    1. Network Traffic Engineering
                                                                      1. Load Balancing
                                                                        1. Quality of Service Improvement
                                                                      2. Chemistry
                                                                        1. Molecular Structure Analysis
                                                                          1. Chemical Compound Representation
                                                                            1. Molecular Symmetry
                                                                              1. Structural Isomer Comparison
                                                                              2. Chemical Graph Theory
                                                                                1. Chemical Bonding Patterns
                                                                                  1. QSPR/QSAR Models
                                                                                2. Operations Research
                                                                                  1. Optimization Problems
                                                                                    1. Linear Programming with Network Constraints
                                                                                      1. Integer Programming in Network Design
                                                                                      2. Facility Layout Planning
                                                                                        1. Material Handling Systems
                                                                                          1. Workflow Optimization
                                                                                            1. Production Line Graph Models
                                                                                        4. Advanced Topics in Graph Theory
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