Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields
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) group $S(\Gamma)$ of $\Gamma$. We determine $S(\Gamma)$ of the generalized de Bruijn graphs $\Gamma=\mathrm{DB}(n,d)$...
| Hlavní autoři: | , , |
|---|---|
| Médium: | Journal article |
| Vydáno: |
2014
|