The basic concept of the graph theory of discrete mathematics

Recently in the chapter on the graph theory of discrete mathematics, here is my classification and summary of some important concepts of the graph.

Describe the concept of relationships

Association--used to describe the relationship between a point and an edge, which simply means that the edge is made up of those points and is associated with those points. The correlation matrix is a matrix that records the number of points in the Edge Association.

adjacency, adjacent--is used to describe the relationship between points and points, forming two points of an edge, which we call adjacency. The adjacency matrix is a matrix that records the number of edges between two points. Special: If this edge is a ring, that is, it is composed of a point, only the beginning and end of the coincidence, then we call the beginning and end of the adjacent.

As shown in figure:
Some of the concepts of the graph are directed to the graph: each edge has a direction of the graph without the map: Similarly, each edge has no direction of the graph mixed graph: Some edges are not directed, some edges are directed to Figure 0 diagram: A graph consisting of isolated nodes (isolated nodes are points that are not adjacent to any nodes in the diagram) Trivial diagram: A 0-figure (n,m) graph with only one node: a graph with n nodes, M-bars: a graph with parallel edges: A simple diagram with no parallel edges: A line chart without a loop (the concept of a ring is referenced above)
(PS: The parallel edges in the figure are different from the parallel edges that we usually understand, the parallel edges in the figure are the two nodes, which are called parallel edges, and if the graph has a direction, then it is required that the sides have the same direction, which is the parallel edge.) See picture below)

Regular graphs: graphs with the same degree of each node are called regular graphs. The graph of each node's degree of K is called the K-order regular graph.

Full picture: Simply put, there is a graph of edges at any point and other points in the graph. Mathematical language: The figure G is an n-order non-simple graph (the concept of a graph similar), if any of the nodes in G and the rest of the n-1 nodes adjacent to the other, then G is the N-order of the non-full graph, recorded as KN. (See the KN in the diagram later, remember that this is a complete representation of the graph, do not be silly kk).

Connected graph, non-connected graph: If the undirected graph G is a trivial graph or any two vertices in G are connected, then the G is a connected graph; otherwise, the G is a non-connected graph. some important theorem : the sum of the degrees of all vertices equals to twice times the number of edges in any graph, the number of vertices with odd degrees is even