On a poset of trees

@article{Csikvri2010OnAP,
  title={On a poset of trees},
  author={P{\'e}ter Csikv{\'a}ri},
  journal={Combinatorica},
  year={2010},
  volume={30},
  pages={125-137}
}
We will prove that the path minimizes the number of closed walks of length l among the connected graphs for all l. Indeed, we will prove that the number of closed walks of length l and many other properties such as the spectral radius, Estada index increase or decrease along a certain poset of trees. This poset is a leveled poset with path as the smallest element and star as the greatest element. 

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