Graph Theory conclusion, Graph Theory Algorithm

Graph Theory conclusion, Graph Theory Algorithm
The connectivity of a graph has a point with a unique degree of 0 in a non-ring graph, which can be reached by any point (because of the absence of a ring, we can start from any point and go forward, must end at a point with an outbound degree of 0.) any point with a non-Inbound degree of 0 in a directed acyclic graph must start from a point with an inbound degree of 0. (Because there is no ring, it is inevitable to go back from any point with an indegree of 0 to a point with an indegree of 0.) assume that there are n points with an indegree of 0, m points with an exit degree of 0. max (m, n) is the undirected graph of the second problem. If a point is deleted, the graph becomes unconnected, this is called a cut point. In a undirected connected graph, if an edge is not connected after being deleted, the edge is called a bridge.
Introduction 1

Graph Theory is a branch of mathematics. It serves as the research object. Graph in graph theory is composed
A graph composed of a given point and a line connecting two points. This graph is usually used to describe
A specific relationship uses a vertex to represent a thing, and a line connecting two points to represent a relationship between two things.
.

Graph Theory itself is a part of applied mathematics. Therefore, historical theories have been independently developed by many mathematicians.
Created. The Textual records of graph theory first appeared in Euler's discussion in 1736.
The question has a strong background.

Graph theory originated from the famous 7-bridge problem in kunisburg. There are seven bridges on the puleger River in coresburg.
As shown in, A, B, C, and D indicate land.

The problem is that we need to start from any of the four land blocks, use each bridge exactly once, and then return to the starting point. However
Countless attempts failed. Euler solved this problem in 1736. He used the abstract analysis method
This is the first graph theory problem: each land is replaced by a point, and each bridge is connected.
A line between the two vertices is replaced to produce a graph (for example ). Euler's proof
The problem is not solved, and the problem is promoted. It gives a way for a given graph
Rules of travel. This work made Euler the founder of graph theory [and Topology.

In 1859, the English mathematician Hamilton invented a game: using a rule of solid twelve-cubes, its
The 20 vertices mark the world's 20 famous cities and ask the players to find one that matches each vertex along each side
One closed loop, that is, "bypassing the world 」. In graph theory, the game aims
The figure shows a generated circle. This problem was later called the Hamilton problem. Caused by operations research and Computer Science
And many problems in the coding theory can be converted into the Hamilton problem, which caused widespread attention and research.

In the history of graph theory, the most famous question is the four-color conjecture. This conjecture says that in a plane
Or any map on the sphere can be colored in only four colors, so that no two neighboring countries have the same
Color. Each country must be composed of a single connected domain, and two neighboring countries mean that they have a public
Boundary, not just a public point. The four-color conjecture has an interesting history. Each map can be exported
In a diagram, all countries are vertices. When the two neighboring countries, the two vertices are connected by a line. Institute
4-color conjecture is a problem in graph theory. Graph Coloring theory, planimetric theory, and algebraic topology graph theory
And other branches.

The wide application of graph theory has promoted its own development. In 1940s, the pseudo-Array Theory and hypermap Theory
Polar Graph theory, as well as algebraic graph theory, topological graph theory, and so on.

Set Graph Theory

Graph Theory is an integral part of discrete mathematics.
Discrete Mathematics is composed of set theory, graph theory, algebraic structure, combined mathematics, and mathematical logic.
Set Theory: set and its operation, binary relationship and function, natural number, natural number set, set base
Graph Theory: basic concepts of graphs, Euclidean and Hamilton graphs, tree and graph Matrix Representation, Dominant Set, overlay set, independent set and matching, weighted graph and Its Application