Example: undirected graph G=(V, E), V is the set of all vertices (non-empty) of the graph, and E is the set of all edges of the graph.
[subgraph and spanning subgraph]
G'=(V', E'), V' is included in V, E' is included in E, and G' is a subgraph of G.
In addition, there is a concept of generating subgraphs for subgraphs, and the difference is: in subgraphs, E'<=E and V'<=V; in generating subgraphs, E'<=E, and V' =V.
【Induced subgraph】
G'=(V', E'), V' is contained in V, E'={(u, v)|u, v belongs to V', (u, v) belongs to E}, G' is the induction of G subgraph.
Note: For V', as long as there is an edge in G, then there should also be an edge in G'.
【Group (clique)】
G' is a complete graph about V'.
A clique is a maximal clique if and only if it is not a subgraph of any other clique.
A graph is a maximum clique if and only if its point set norm is the largest.
The number of cliques in a graph is denoted ω(G).
【minimum coloring】
Color the points with the smallest color to make adjacent points different colors. The number of colors at this time is called chromatic number.
The chromatic number of a graph is denoted by χ(G).
[maximum independent set]
The largest subset of points is such that no two points are adjacent. Denoted as α(G).
[minimum clique cover]
Cover all points with the least number of clumps. Denoted as κ (G).
【chord】
An edge connecting two points in a ring that are not adjacent.
【弦图（chordal graph）】
An undirected graph is called a chord graph when any cycle of length greater than 3 in the graph has at least one chord.
【simplicial vertex】
Let N(v) denote the set of points adjacent to point v. A point is called a simple point when the induced subgraph of {v}+N(v) is a clique.
[theorem]
Any chord graph has at least one simple point, and a chord graph that is not complete has at least two non-adjacent simple points.
[perfect elimination ordering]
A sequence of points (each point occurs exactly once) v[1], v[2], ..., v[n] such that v[i] is in {v[i], v[i+1] , ..., v[n]} is a simple point in the induced subgraph.
Reprinted from: http://www.cnblogs.com/zxfx100/archive/2011/03/23/1993055.html
来自：On the Approximability of NP-complete Optimization Problems