Thesis ID: CBB786501063

An Exploration of the Matching Polynomial (2023)


The matching polynomial for graphs was defined by Farrell in a paper published in 1979 as an invariant for graphs with fixed edge and vertex weights. However, the same polynomial had been modeled before and since by scientists in other disciplines; in particular, the matching polynomial models monomer-dimer systems, which are of interest in physics, and the polynomials studied in rook theory are actually matching polynomials of bipartite graphs. We take interest in Farrell’s definition of the matching polynomial and prove many results from his first paper on the subject, as well as provide some modifications and expansions of his ideas, in Chapter 2. We also explore some features of the more common (non-weighted) matching polynomial, taking particular interest in the relationship between matchings of a graph and matchings of its complement in Chapter 3.

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Authors & Contributors
Biggs, Norman L.
Carter, Jessica
Friedman, Michael L.
Gieemann, Sebastian
Gottschalla, Christian
Mallion, Roger
Historia Mathematica
British Journal for the History of Mathematics
Ambix: Journal of the Society for the History of Alchemy and Chemistry
Archive for History of Exact Sciences
Archives Internationales d'Histoire des Sciences
Massachusetts Institute of Technology, MIT
Cambridge University Press
Princeton University Press
University of Chicago Press
Graph theory
Visual representation; visual communication
Network theory; network analysis
Euler, Leonhard
König, Dénes
Appel, Kenneth
Artin, Emil
Dagognet, Françoise
Dubois, Jacques
Time Periods
20th century
20th century, late
20th century, early
21st century
18th century
19th century
United States
Great Britain

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