Two sets 
and 
are said to be independent if their intersection 
, where 
is the empty
set. For example, 
and 
are independent, but 
and 
are not. Independent sets are also called disjoint
or mutually exclusive.
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 
. The figure above shows independent
vertex sets consisting of two subsets for a number of graphs (the wheel
graph 
,
utility graph 
, Petersen graph, and
Frucht graph).
An independent edge set can be defined similarly (Skiena 1990, p. 219).
A maximal independent set is an independent set which is a maximal set, i.e., an independent set that is not a subset of any other independent set.
