Symmetric Matrices & Quadratic Forms · Superchallenge problem

The Petersen graph has as vertices the ten 2-element subsets of $\{1, 2, 3, 4, 5\}$, two vertices being adjacent when the subsets are disjoint. Find the minimum of $\displaystyle\sum_{\{u, v\}\text{ an edge}}(x_u - x_v)^2$ over all real vectors $(x_v)$ with $\sum_v x_v = 0$ and $\sum_v x_v^2 = 1$.