The Characteristic Polynomial of Multi-Rooted, Directed Trees
We define the characteristic polynomial for single-rooted trees and begin with a theorem about this polynomial, derived from the known contrac- tion/deletion formula. We expand our scope to include multi-rooted, directed trees. Introducing the concept of a star, we prove two theorems which allow us to evaluate the polynomials of these trees in terms of the stars that comprise them. Finally, we derive and prove a general formula for the characteristic polynomial of multi-rooted, directed trees.
Franklin and Marshall College Archives, Undergraduate Honors Thesis 2008
- F&M Theses Collection