Some basic definitions of graph theory __ graph theory

From: http://www.cppblog.com/RyanWang/archive/2009/05/01/81617.html

Standalone set:

A set of independent sets is a subset of the vertex set of a graph, the exported child graph of the subset does not contain edges. If a set of independent sets is not a subset of any set of independent sets, then the independent set is called a maximal independent set. The independent set with the highest number of vertices in a graph is called the maximum independent set. The maximal independent set must be a maximal independent set, but the maximal independent set is not necessarily the largest independent set.

Dominating set:

The corresponding to the independent set is the dominating set, the dominating set is also a subset of the graph vertex set, and the S is a dominating set of graph G, then for any vertex u in the graph, it is either a set S or a vertex adjacent to S. After removing any element in S, S is no longer a dominating set, then the dominating set S is the minimal dominating set. The dominating set with the least number of vertices in all dominating sets of g is the minimum dominating set, and the number of vertices in the minimum dominating set becomes the dominant number.

Overlay of minimum points:

The overlay of the smallest point is also a subset of the vertex set of the graph, and if we select a point, it is said to be covered by all the edges of the endpoint. All the edges in the diagram are covered with the least number of vertices, and this set is the smallest point of coverage.

Max Group:

A subset of the vertices of fig G, set D to be the largest group, then any two points in D are adjacent. If the U,V is the largest group, then the u,v is connected, and the complement graph is u,v without the side connection, so the maximal group of graph G = The maximal independent set of the complement graph.

Some properties:

Maximum independent set + minimal covering set =v

Maximal independent set of maximal group = complement graph

Minimum coverage set = Maximum match