Chromatic polynomials of signed graphs
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, p...
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| Format: | Final Year Project |
| Language: | English |
| Published: |
Nanyang Technological University
2023
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| Online Access: | https://hdl.handle.net/10356/166474 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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