Let G(v,e) be the set of all simple graphs with v vertices and e edges and let P₂(G) = ∑ d_i² denote the sum of the squares of the degrees of the vertices of G. I will classify all graphs G in G(v,e) for which P₂(G) attains a maximum.

This talk is based on a recent paper by Bernardo M. Ábrego, Silvia Fernández-Merchant, Micheal G. Neubauer, and William Watkins.