Middle East Technical University Mathematics Department Seminars

When sparse trees are dense and when trees are indistinguishable
Hua Wang
Georgia Southern University, United States of America
Özet : We will consider two questions proposed by R. Jamison in 1983 regarding the average subtree order of trees. The first question asks if it is true that a tree with internal vertex degree at least 3 has its average subtree order being at least half of the total number of vertices. We provide a positive answer to this question and some further observations on how the trees with large or small average subtree order look like. The second question asks if every two non-isomorphic trees of the same order have different average subtree orders. We provide an example showing that the answer is negative. This example follows from a generalization of Schwenk's classical result on the cospectral mate of a tree.
  Tarih : 10.04.2014
  Saat : 15:40
  Yer : Gunduz Ikeda Room
  Dil : English
  Web : http://math.metu.edu.tr/general-seminars-0
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