A vertex-induced subgraph (sometimes simply called an "induced subgraph") is a subset of the vertices of a graph 
together with any edges whose endpoints are both in this subset.
The figure above illustrates the subgraph induced on the complete
graph 
by the vertex subset 
.
An induced subgraph that is a complete graph is
called a clique. Any induced subgraph of a complete
graph forms a clique. The subgraph induced by a set
of vertices can be computed in the Wolfram
Language using Subgraph[g,
vlist].
A graph is called a perfect graph if, for each of its induced subgraphs 
,
the chromatic number of 
equals the largest number of pairwise adjacent vertices
in 
.
The cube polynomial encodes the numbers of vertex-induced subgraphs of a graph that are isomorphic to hypercube graphs.
The number of 
-cycles in a graph can be determined using its connected
induced subgraphs (Giscard et al. 2016).
