Individual summary of "discrete Mathematics 2" algebra system and Graph theory

Source: Internet
Author: User

Algebraic system part

The principle of pigeon nest based on basic theorem

    • Group theory
    1. Guang Qun
    2. Semi-group
    3. Different points
    4. Group
      1. The order of the Group and the Order of the elements
      2. Accompany set and Lagrange theorem
      3. Special groups
        1. Exchange/Abelian group
        2. Cyclic group
    5. Sylow theorem
    • Rings and fields
    1. Ring
    2. Whole ring
    3. Domain
    • Lattice theory
    1. Pane
    2. Allocation grid
    3. Die Lattice
    4. A bounded lattice
    5. Patch

Part of the graph theory

The theorem of basic theorem handshake

Handshake theorem, there are n personal handshake, each handshake x times, the total number of handshakes for s= NX/2.

The relationship between the degree and the number of edges of the graph

    • Basic concepts
    1. The path node alternates with adjacent edges V0E1V1E2...VN-1ENVN
    2. Circuit V0=VN Road//A textbook although it is written but the problem is the Euler circuit OH
    3. Pathway
    4. Circle
    5. Trace
    6. Closed Trace
    • Representation of graphs
    1. Adjacency Matrix
    2. Correlation matrix (horizontal longitudinal point, direction Graph 1 in-1
    • The connectivity of graphs
    1. Non-Tourienton/non-connected
    2. Forward graph strong connectivity/single-sided connectivity/weak connectivity
    3. Proof method: Specific analysis of the special case of the Reach matrix (Eulerian graph has the necessary and sufficient conditions, Hamilton full/essential
    • Eulerian Graph/Hamilton Map
    1. Oralu sufficient and necessary conditions: 1. Connect Figure 2.0or2 of ODD nodes
    2. Sufficient and necessary conditions for Euler loops: 1. Connect Figure 2. All the nodes are even
    3. Hamilton Road Requirements: W (g-s) <=| S|+1
    4. Hamilton Road full condition: Any pair of nodes with degrees and greater than or equal to n-1
    5. Hamilton Circuit Requirements: W (g-s) <=| s|
    6. Hamilton Loop sufficient condition: any pair of node degrees and greater than equals n
    • Two part diagram
    • Floor plan
    1. Euler theorem v-e+r=2 for planar connected graphs
    2. Its inference (+2e>=3r) e<=3v-6
    3. Kuratowski theorem k3,3 K5 two degree in-node isomorphism
    • Tree
    1. Spanning tree
    2. Minimum spanning tree
    3. There is a direction to the tree
    4. Genchu
      1. Full m fork Tree K Branch node internal path and I, external path and E e=mk+ (m-1) I
      2. Regular m fork Tree

Individual summary of "discrete Mathematics 2" algebra system and Graph theory

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