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Title:
Old and New Results on the Spread of the Spectrum of a Graph
Speaker:
Abstract:
The spread of a matrix is defined as the diameter of its spectrum. This quantity has been well-studied for general matrices and has recently grown in popularity for the specific case of the adjacency matrix of a graph. Most notably, Gregory, Herkowitz, and Kirkland proved a number of key results for the spread of a graph and made two key conjectures regarding graphs that maximize spread. In particular, they conjectured that the maximum spread over all graphs with a fixed number of vertices is given by the join of a clique and independent set and that the maximum spread over all graphs with a fixed number of vertices and edges is given by a bipartite graph if one exists. In this talk, I will review some of the key results regarding the spread of a general matrix, some known results for the specific case of an adjacency matrix, and give a high-level outline of a recent paper regarding these two conjectures. This is joint work with Jane Breen, Alex Riasanovsky, and Michael Tait.
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