Turan's graph theorem and maximum independent sets in Brandt semigroups

Let B-n be an aperiodic Brandt semigroup M-0[G; n, n; P] where G is the trivial group, n is an element of N and P = (a(ij))(n x n) with a(ij) = 1(G) if i = j and a(ij) = 0 otherwise. The maximum size of an independent set in B-n is known to be [n(2)/4] + n, where [n(2)/4] denotes the largest integer not greater than n2/4. We reprove this result using Turin's famous graph theorem. Moreover, we give a characterization of all independent sets in 93, with size [n(2)/4] + n.