Hicks, Illya V2017-07-312017-07-312015-122015-10-13December 2Brimkov, Boris. "Efficient Computation of Chromatic and Flow Polynomials." (2015) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/95530">https://hdl.handle.net/1911/95530</a>.https://hdl.handle.net/1911/95530This thesis surveys chromatic and flow polynomials, and presents new efficient methods to compute these polynomials on specific families of graphs. The chromatic and flow polynomials of a graph count the number of ways to color and assign flow to the graph; they also contain other important information such as the graph's chromatic number, Hamiltonicity, and number of acyclic orientations. Unfortunately, these graph polynomials are generally difficult to compute; thus, research in this area often focuses on exploiting the structure of specific families of graphs in order to characterize their chromatic and flow polynomials. In this thesis, I present closed formulas and polynomial-time algorithms for computing the chromatic polynomials of novel generalizations of trees, cliques, and cycles; I also use graph duality to compute the flow polynomials of outerplanar graphs and generalized wheel graphs. The proposed methods are validated by computational results.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Chromatic polynomialflow polynomialThesis2017-07-31