The (upper) clique number of a graph 
, denoted 
, is the number of vertices in a maximum
clique of 
.
Equivalently, it is the size of a largest clique or maximal clique of 
.
The clique number 
of a graph is equal to the largest exponent in the graph's clique
polynomial.
The lower clique number 
may be similarly defined as the size of a graph's
smallest maximal clique.
For an arbitrary graph,
 |
(1)
|
where 
is the vertex degree of 
.
The clique number of a graph is equal to the independence number of the complement graph,
 |
(2)
|
The chromatic number 
of a graph 
is equal to or greater than its clique number 
, i.e.,
 |
(3)
|
The following table lists the clique numbers for some named graphs.
