Project: Section 1.3 focuses on using unlabeled, unrooted trees to model RNA secondary structure. However, rooted and/or labeled trees can also be used to model important aspects of RNA secondary structure. Explore this idea and how it affects the estimates of the number of possible RNA secondary structure techniques. As part of this exploration, consider the following:

a. Select biologically relevant information to use as vertex labels. What labels did you choose and why? What other choices might you have made?

b. Compare counts for trees, rooted trees, and labeled trees. (Work through some examples for small numbers of vertices. Research the formulas for these counts for large values.)