The sum of squares of degrees of bipartite graphs

Let G be a subgraph of the complete bipartite graph K-l,K-m, l <= m, with e = qm + p > 0, 0 <= p < m, edges. The maximal value of the sum of the squares of the degrees of the vertices of Gisqm(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.

Automated summary

This passage discusses the properties of the complete bipartite graph and its subgraph G, as well as the maximum value of the sum of the squares of the degrees of the vertices. It also classifies all graphs that reach this bound using the diagonal sequence of a partition.