  We consider the problem of computing the second elementary symmetric
polynomial S^2_n(X) using depth-three arithmetic circuits of the form "sum of
products of linear forms". We consider this problem over several fields and
determine EXACTLY the number of multiplication gates required. The lower bounds
are proved for inhomogeneous circuits where the linear forms are allowed to
have constants; the upper bounds are proved in the homogeneous model. For reals
and rationals, the number of multiplication gates required is exactly n-1; in
most other cases, it is \ceil{n/2}. This problem is related to the
Graham-Pollack theorem in algebraic graph theory. In particular, our results
answer the following question of Babai and Frankl: what is the minimum number
of complete bipartite graphs required to cover each edge of a complete graph an
odd number of times? We show that for infinitely many n, the answer is
\ceil{n/2}.
