Tutte Polynomials of Some Graphs

ECSU Author/Contributor (non-ECSU co-authors, if there are any, appear on document)
Anthony Meadows, student (Creator)
Julian A. D. Allagan , Associate Professor (Contributor)
Elizabeth City State University (ECSU )
Web Site: https://www.ecsu.edu/academics/library/index.html

Abstract: Given any graph G, there is a bivariate polynomial called Tutte polynomial which can be derived from G. We denote such polynomial by T(G; x; y). This thesis introduces the two techniques commonly used to compute T(G; x; y) along with several examples. Further, we determine T(G; x; y) for various classes of graphs such as cycles, trees, cacti, (2; 2; 1), which is a multi-bridge graph, and the well-known Peterson graph. We plot these surfaces, their contours and, for each such graph G, weevaluate their T(G; x; y) for some values (x; y) along a curve. We obtain important information about these graphs namely the number of spanning trees and number of spanning subgraphs. We also introduced some related polynomials such as thechromatic polynomial, the flow polynomial and the reliability polynomial.

Additional Information

Language: English
Date: 2020
polynomials, graphs, math theorems

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