Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields

Swee Hong Chan, Henk D. L. Hollmann, Dmitrii V. Pasechnik

A maximal minor $M$ of the Laplacian of an $n$-vertex Eulerian digraph $\Gamma$ gives rise to a finite group ${\mathbb{Z}}^{n-1}/{\mathbb{Z}}^{n-1}M$ known as the sandpile (or critical) gro…