Seminar: Independence Equivalence Classes of Paths and Cycles
- Date
- February 26, 2020
- Time
- 11:00 AM EST - 12:00 PM EST
- Location
- ENG 210
- Open To
- All faculty, staff, students and guests are welcome to attend.
The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size. The independence equivalence class of a graph is the class of all graphs that share its independence polynomial. In this talk we will consider independence equivalence classes of paths (Pn) and cycles (Cn). We completely determine the independence equivalence class of Pn when n is odd and partial results for when n is even give a surprising contrast. For cycles, we completely determine the independence equivalence class of Cn when n is even or n=pk for all primes p>3 and integers k>= 1. The proofs involve combinatorial techniques as well as techniques for locating the roots and determining the reducibility of the polynomials.
(This is a joint work with Iain Beaton and Jason Brown.)