This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# IndependentVertexSetQ

 IndependentVertexSetQ yields True if the vertex list vlist is an independent vertex set in the graph g and False otherwise.
• An independent vertex set is a set of vertices that are never incident to the same edge.
Test whether a set of vertices is an independent vertex set:
Test for a directed graph:
Test whether a set of vertices is an independent vertex set:
 Out[1]=
 Out[2]=

Test for a directed graph:
 Out[1]=
 Out[2]=
 Scope   (2)
Test undirected graphs:
Directed graphs:
 Applications   (2)
Enumerate all independent vertex sets for a cycle graph:
Enumerate all subsets of vertices and select the ones that are independent vertex sets:
Highlight independent vertex sets:
Enumerate all maximal independent vertex sets for a Petersen graph:
Find the size of a maximal independent vertex set:
Enumerate all maximal independent vertex sets:
Highlight maximal independent sets:
A largest independent vertex set can be found using FindIndependentVertexSet:
The complement of an independent vertex set is a vertex cover:
The complement subgraph given by an independent vertex set is complete:
Bipartite graphs have equal-length edge covers and independent vertex sets:
New in 8