#### 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