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Math & Stats Number Theory Seminar
Thursday, October 10th, 2024

Time: 4:30 p.m.  Place: Jeffery Hall, Room 202

Speaker: Becca Carter (³ÉÈË´óƬ)

Title: Diameters of directed graphs

Abstract: This talk explores spectral bounds on the diameter of graphs, with a focus on both undirected and directed graphs. I will present two key results: an improved spectral bound for undirected graphs and a novel bound for directed graphs. The improved bound for undirected graphs refines the classic result of Fan Chung from her 1989 paper "Diameters and Eigenvalues". For directed graphs, we introduce a new spectral bound using similar techniques. Central to both results is the representation of graphs as Markov chains, leveraging the transition matrix to derive bounds on the diameter. This spectral approach offers new insights into the structural properties of graphs, with potential applications in network theory.