  Motivated by the study of the crossing number of graphs, it is shown that,
for trees, the sum of the products of the degrees of the end-vertices of all
edges has an upper bound in terms of the sum of all vertex degrees to the power
of $\phi^2$, where $\phi$ is the golden ratio. The exponent $\phi^2$ is best
possible. This inequality is generalized for all graphs with bounded maximum
average degree.
