Chromatic polynomials of signed graphs

• Main Author: Utomo, Charissa Irene
• Other Authors: Gary Royden Watson Greaves
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Science::Mathematics::Discrete mathematics::Graph theory
• Online Access: https://hdl.handle.net/10356/166474
• Institution: Nanyang Technological University

Signed graphs are currently enjoying intense interest from the combinatorial community due to various mathematical breakthroughs that relied on results about signed graphs. We expose the discrepancies in the computation of the chromatic polynomials of signed Complete Graphs and Petersen Graphs, presented in the research paper titled “The Chromatic Polynomials of Signed Petersen Graphs” by Beck et al. This research paper aims to address and correct the disparities in “The Chromatic Polynomials of Signed Petersen Graphs”. Moreover, we exhibit a SageMath code implementation to efficiently compute the chromatic polynomials of signed graphs with the input of adjacency matrices. We independently develop the concept of bivariate chromatic polynomials in signed graphs in order to determine the chromatic polynomials of the subgraphs within the signed graph. Notably, our original contribution involves the derivation of explicit formulas to chromatic polynomials of some families of signed graphs. Furthermore, we express the even and odd chromatic polynomials simultaneously through quasipolynomials.