3 papers
math.CO2023
Bounds on Kemeny's constant of a graph and the Nordhaus-Gaddum problem
Sooyeong Kim, Neal Madras, Ada Chan +3
We study Nordhaus-Gaddum problems for Kemeny's constant of a connected graph . We prove bounds on and the pro…
math.SP2023
Completion Problems and Sparsity for Kemeny's Constant
Stephen Kirkland
For a partially specified stochastic matrix, we consider the problem of completing it so as to minimize Kemeny's constant. We prove that for any partially specified stochastic matr…
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…