Discrete & Computational Math Seminar: Cyclotomic Matrices and Graphs with q=2

Discrete & Computational Math Seminar (DisCoMath)
Cyclotomic Matrices and Graphs with q=2
Brendan Rooney
School of Mathematical Sciences, RIT

Abstract:
We survey a sequence of papers by Smyth, McKee, Greaves, and Taylor on Lehmer's Conjecture and cyclotomic matrices. Our focus is the graphs corresponding to maximal indecomposable cyclotomic matrices (GMICs for short). For a graph 𝐺, the value 𝑞(𝐺) is the smallest number of distinct eigenvalues of a symmetric matrix 𝑀 whose off-diagonal zero pattern matches that of the adjacency matrix of 𝐺 exactly. Recent work on sparse graphs, and 4-regular graphs, with 𝑞(𝐺)=2 reveals that most of these 𝑞=2 graphs correspond to GMICs. This talk is part of an attempt to connect these bodies of work, and will contain open questions.

Speaker Bio:
See bio here.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

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