Enumerating Unlabeled Trees
At the Nebraska Conference for Undergraduate Women in Mathematics (big related announcement to come soon) in January, I presented part of my thesis work. The following abstract summarizes what I talked about. The presentation was mostly just for visuals, so you will have to wait until my final thesis is published to read more & fill in some of the blanks.
One of the earliest papers on graph theory was written by Euler in 1736. Since then, graphs have been studied by the likes of Foster, Coxeter, Biggs, and Peterson. Applications extend beyond the world of pure mathematics into the areas of engineering, computer programming, chemistry, and more. Yet, after three hundred years of intense study, there are many problems that are open or in need of improvements. In this talk, we will examine an improved algorithm that we developed for counting the number of unlabeled trees where the degree of each vertex is less than or equal to four, which translates into counting the number of isomers of alkanes.
Enumerating Unlabeled Trees (pdf of presentation slides)