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Explore the intersection of graph theory and chemistry in this 47-minute seminar that demonstrates how mathematical modeling can illuminate molecular structures and properties. Learn how graphs serve as powerful visual tools for representing complex phenomena by using points and lines to focus on essential elements while eliminating unnecessary details. Discover the field of graph chemistry, also known as topological chemistry, which applies graph theory principles to model molecular structures where atoms are represented as vertices and chemical bonds as edges. Examine how degree-based topological indices function as molecular descriptors for studying physicochemical properties, computed from bond weights determined by formulas based on endpoint degrees. Investigate the mathematical problem of finding molecules with specific numbers of atoms and bonds that maximize or minimize given topological indices, with particular focus on conjugated systems including alkenes, polyenes, benzenoids, and fullerenes. Understand how this optimization problem reduces to determining extreme points of a polytope with at most 10 facets, and discover the remarkable finding that regardless of the chosen degree-based topological index, there are at most 16 extreme points, meaning very few different classes of extremal molecules exist for any given molecular size and bond count.
