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math-ph2023
Nodal decompositions of a symmetric matrix
Theo McKenzie, John Urschel
Analyzing nodal domains is a way to discern the structure of eigenvectors of operators on a graph. We give a new definition extending the concept of nodal domains to arbitrary sign…
math.CO2023
Explicit two-sided unique-neighbor expanders
Jun-Ting Hsieh, Theo McKenzie, Sidhanth Mohanty +1
We study the problem of constructing explicit sparse graphs that exhibit strong vertex expansion. Our main result is the first two-sided construction of imbalanced unique-neighbor…