The Haemers number of an 
-vertex
graph 
,
denoted 
,
(Alipour abd Gohari 2023), or 
(Haemers 1978), is an integer defined
as the minimum rank over all 
matrices 
over some field such that 
and 
if vertices 
and 
are not adjacent in a given graph 
. (Note that the critical word "not" was inadvertently
omitted in the original Haemers (1978) paper.)
The Haemers number provodes upper bound on the Shannon capacity of 
which is sometimes better than the Lovász number.
The Haemers number satisfies
 |
(Haemers 1978), where 
is the chromatic number and 
denotes the graph complement
of 
.
