Title
When Sparse Trees Are Dense and When Trees Are Indistinguishable
Document Type
Presentation
Publication Date
4-10-2014
Abstract
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.
Sponsorship/Conference/Institution
Middle East Technical University
Location
Ankara, Turkey
Recommended Citation
Wang, Hua.
2014.
"When Sparse Trees Are Dense and When Trees Are Indistinguishable."
Mathematical Sciences Faculty Presentations.
Presentation 543.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/543