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math.CO2023
Powers of Karpelevic arcs and their Sparsest Realising matrices
Priyanka Joshi, Stephen Kirkland, Helena Smigoc
The region in the complex plane containing the eigenvalues of all stochastic matrices of order n was described by Karpelevic in 1988, and it is since then known as the Karpelevic r…
math.CO2023
Edge Addition and the Change in Kemeny's Constant
Stephen Kirkland, Yuqiao Li, John McAlister +1
Given a connected graph , Kemeny's constant measures the average travel time for a random walk to reach a randomly selected vertex. It is known that when an e…
math.CO2013★ 1 cited
alpha-Kuramoto partitions: graph partitions from the frustrated Kuramoto model generalise equitable partitions
Stephen Kirkland, Simone Severini
The Kuramoto model describes the collective dynamics of a system of coupled oscillators. An alpha-Kuramoto partition is a graph partition induced by the Kuramoto model, when the os…