The maximum possible weight of a fractional clique of a graph 
is called the fractional clique number of 
, denoted 
(Godsil and Royle 2001, pp. 136-137) or 
(Larson et al. 1995). Every simple graph has a fractional clique number which
is a rational number or integer.
The fractional clique number satisfies
 |
where 
is the clique number, 
is the fractional
chromatic number, and 
is the chromatic number
(Godsil and Royle 2001, pp. 141 and 145), where the result 
follows from the strong duality theorem
for linear programming (Larson et al. 1995; Godsil and Royle 2001, p. 141).
