Discrete Mathematics

  1. Graph Theory
    1. Graph Fundamentals
      1. Basic Definitions
        1. Graphs and Vertices
          1. Edges and Adjacency
            1. Degree of Vertices
              1. Handshaking Lemma
              2. Types of Graphs
                1. Simple Graphs
                  1. Multigraphs
                    1. Directed Graphs
                      1. Weighted Graphs
                        1. Complete Graphs
                          1. Bipartite Graphs
                            1. Regular Graphs
                            2. Graph Representations
                              1. Adjacency Matrix
                                1. Adjacency List
                                  1. Incidence Matrix
                                    1. Edge List
                                  2. Graph Connectivity
                                    1. Paths and Walks
                                      1. Walks, Trails, and Paths
                                        1. Cycles and Circuits
                                          1. Distance in Graphs
                                          2. Connected Graphs
                                            1. Connected Components
                                              1. Cut Vertices
                                                1. Bridges
                                                  1. Vertex and Edge Connectivity
                                                  2. Euler Paths and Circuits
                                                    1. Eulerian Graphs
                                                      1. Euler's Theorem
                                                        1. Finding Euler Paths
                                                        2. Hamilton Paths and Circuits
                                                          1. Hamiltonian Graphs
                                                            1. Necessary Conditions
                                                              1. Sufficient Conditions
                                                                1. Traveling Salesman Problem
                                                              2. Graph Algorithms
                                                                1. Graph Traversal
                                                                  1. Applications of Traversal
                                                                  2. Shortest Path Algorithms
                                                                    1. Dijkstra's Algorithm
                                                                      1. Bellman-Ford Algorithm
                                                                        1. Floyd-Warshall Algorithm
                                                                        2. Minimum Spanning Trees
                                                                          1. Kruskal's Algorithm
                                                                            1. Prim's Algorithm
                                                                              1. Properties of MSTs
                                                                              2. Network Flow
                                                                                1. Maximum Flow Problem
                                                                                  1. Ford-Fulkerson Algorithm
                                                                                2. Special Graph Topics
                                                                                  1. Graph Coloring
                                                                                    1. Vertex Coloring
                                                                                      1. Chromatic Number
                                                                                        1. Edge Coloring
                                                                                          1. Planar Graph Coloring
                                                                                            1. Four Color Theorem
                                                                                            2. Planar Graphs
                                                                                              1. Definition and Properties
                                                                                                1. Euler's Formula
                                                                                                  1. Kuratowski's Theorem
                                                                                                    1. Dual Graphs
                                                                                                    2. Graph Isomorphism
                                                                                                      1. Definition and Testing
                                                                                                        1. Automorphisms
                                                                                                          1. Graph Invariants

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                                                                                                      6. Trees