Minimum algebraic connectivity and maximum diameter: Aldous--Fill and Guiduli--Mohar conjectures

Maryam Abdi, Ebrahim Ghorbani

Aldous and Fill (2002) conjectured that the maximum relaxation time for the random walk on a connected regular graph with $n$ vertices is $(1+o(1))\frac{3n^2}{2{\pi }^2}$. A conjec…