#### Title

On the Local and Global Means of Subtree Orders

#### Document Type

Article

#### Publication Date

2-2016

#### Publication Title

Journal of Graph Theory

#### DOI

10.1002/jgt.21869

#### ISSN

1097-0118

#### Abstract

The global mean of subtrees of a tree is the average order (i.e., average number of vertices) of its subtrees. Analogously, the local mean of a vertex in a tree is the average order of subtrees containing this vertex. In the comprehensive study of these concepts by Jamison (J Combin Theory Ser B 35 (1983), 207–223 and J Combin Theory Ser B 37 (1984), 70–78), several open questions were proposed. One of them asks if the largest local mean always occurs at a leaf vertex. Another asks if it is true that the local mean of any vertex of any tree is at most twice the global mean. In this note, we answer the first question by showing that the largest local mean always occurs at a leaf or a vertex of degree 2 and that both cases are possible. With this result, a positive answer to the second question is provided. We also show some related results on local mean and global mean of trees.

#### Recommended Citation

Wagner, Stephen, Hua Wang.
2016.
"On the Local and Global Means of Subtree Orders."
*Journal of Graph Theory*, 81 (2): 154-166.
doi: 10.1002/jgt.21869

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/334