On a poset of trees

Abstract

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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Correspondence to Péter Csikvári.

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While this paper was carried out the author was the guest of the University of Memphis.

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Csikvári, P. On a poset of trees. Combinatorica 30, 125–137 (2010). https://doi.org/10.1007/s00493-010-2516-0

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Mathematics Subject Classification (2000)

  • 05C05
  • 05C35