## What else is new on subtrees of trees

- March 19, 2012
- 3:50 p.m.
- LeConte 314D

## 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 Schwenkâ€™s classical result on the cospectral mate of a tree.