#### Graduation Year

2015

#### Document Type

Open Access Senior Thesis

#### Degree Name

Bachelor of Science

#### Department

Mathematics

#### Reader 1

Mohamed Omar

#### Reader 2

Michael Orrison

#### Rights Information

© 2015 Jazmin S Ortiz

#### Abstract

The chromatic polynomial of a graph, is a polynomial that when evaluated at a positive integer k, is the number of proper k colorings of the graph. We can then find the orbital chromatic polynomial of a graph and a group of automorphisms of the graph, which is a polynomial whose value at a positive integer k is the number of orbits of k-colorings of a graph when acted upon by the group. By considering the roots of the orbital chromatic and chromatic polynomials, the similarities and differences of these polynomials is studied. Specifically we work toward proving a conjecture concerning the gap between the real roots of the chromatic polynomial and the real roots of the orbital chromatic polynomial.

#### Recommended Citation

Ortiz, Jazmin, "Chromatic Polynomials and Orbital Chromatic Polynomials and their Roots" (2015). *HMC Senior Theses*. 92.

https://scholarship.claremont.edu/hmc_theses/92