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

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