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
