The Haemers number of an n-vertex graph G, denoted H(G), ℋ(G) (Alipour abd Gohari 2023), or R(G), is an integer defined as the minimum rank over all n×n matrices B over some field such that b_(i i) !=0 and b_(i j) = 0 if vertices i and j are not adjacent in a given graph G. (Note that the critical word "not" was inadvertently omitted in the original Haemers paper.) The Haemers number provodes upper bound on the Shannon capacity of G which is sometimes better than the Lovász number.

Lovász number | Shannon capacity