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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.

Thanks for your comments in advance

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    $\begingroup$ I don't understand your question. The sum of the eigenvalues of the Laplacian of a graph with m edges is always 2m. So what exactly are you trying to optimize? $\endgroup$
    – Casteels
    Commented May 31, 2013 at 19:25
  • $\begingroup$ @Casteels: You're right. I edit my question. $\endgroup$
    – Royeh
    Commented May 31, 2013 at 21:53
  • $\begingroup$ So, for example, for fixed $n$, you want to characterize the trees on $n$ vertices whose sum of first $k$ eigenvalues is maximum? $\endgroup$
    – Casteels
    Commented Jun 1, 2013 at 15:12
  • $\begingroup$ @Casteels: yes, that's what I want to do. I am trying to start from a simple cycle and with knowing symmetric properties expand my work to trees and some other class of graphs. $\endgroup$
    – Royeh
    Commented Jun 3, 2013 at 20:20

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