The sum of squares of degrees of bipartite graphs.

Let G be a subgraph of the complete bipartite graph K l , m , l ≤ m , with e = q m + p > 0 , 0 ≤ p < m , edges. The maximal value of the sum of the squares of the degrees of the vertices of G is q m 2 + p 2 + p (q + 1) 2 + (m - p) q 2 . We classify all graphs that attain this bound using the diagonal sequence of a partition. [ABSTRACT FROM AUTHOR]