An independent vertex set of a graph 
is a subset of the vertices such that no two vertices in the
subset represent an edge of 
. Given a vertex cover of a
graph, all vertices not in the cover define a independent
vertex set (Skiena 1990, p. 218). A maximum independent vertex set is an independent
vertex set containing the largest possible number of vertices for a given graph.
A maximum independent vertex set is not equivalent to a maximal independent vertex set, which is simply an independent vertex set that cannot be extended to a larger independent vertex set. Every maximum independent vertex set is also an independent vertex set, but the converse is not true.
The independence number of a graph is the cardinality of the maximum independent set.
Maximum independent vertex sets correspond to the complements of minimum vertex covers.
A maximum independent vertex set in a given graph 
can be found in the Wolfram Language
using FindIndependentVertexSet[g][[1]].
The command Sort[FindIndependentVertexSet[g,
Length /@ FindIndependentVertexSet[g], All]] will
find all maximum independent vertex sets.
