# Optimization over Spectral Laplacian in cycles and trees

Is there any idea on how one can deal with an optimization problem of sum of k largest eigenvalues(min) of Laplacian matrix of a simple cycle or tree? I would like to use semidefinite programming for modeling as it's mentioned in Alizadeh's paper.

So, for example, for fixed $n$, you want to characterize the trees on $n$ vertices whose sum of first $k$ eigenvalues is maximum? – Casteels Jun 1 '13 at 15:12