Nonsingularity of adjacency matrices of random $r$-regular graphs

Hoi H. Nguyen, Melanie Matchett Wood

Published 2018-06-26Version 1

We prove that the adjacency matrices of uniform random r-regular graphs on n vertices are asymptotically almost surely nonsingular for even n. We use recent mixing results of M\'esz\'aros for adjacency matrices of certain random r-regular multi-graphs and results of the second author on the moment problem for random finite abelian groups.