Counting Subtrees: Enumerative and Extremal Questions

<div class="line" id="line-5"> The subtrees of a tree have been studied from various points of view. In particular, the extremal trees that maximize the number of subtrees were identi&filig;ed for different categories of trees such as binary trees and trees with a given maximum degree. We extend these results to trees with given degree sequences. Furthermore, an ordering of the extremal trees with different degree sequence is provided. This ordering provides a relatively easy way to identify extremal trees. Some of the previously know results follow as corollaries.</div>