In the paper "[On the Sandpile Group of a Graph](https://www.semanticscholar.org/paper/On-the-Sandpile-Group-of-a-Graph-Cori-Rossin/6e6b54f13fbc93a91e351133f0c5c3de9fb2c1a7)" by Cori and Rossin one can find a result related to the structure of the sandpile group of $W\_n$. Is there a way to provide a set of generators in parametric form in both the cases when $n$ is even/odd?


Update #1: the identity is known (source is coming), that is the all 2's configuration. Numerical experience suggests that in case of even values of $n$ two configurations generating the group are $(1,2,1,\ldots),(2,1,1,\ldots),$ in case of odd values these are $(2,1,1,\ldots),(2,2,1,\ldots).$ Probably it is also known, however I have not found yet.


Update #2: Biggs: "[Chip-Firing and the Critical Group of a Graph](https://link.springer.com/article/10.1023/A:1018611014097)" provides generators as well.



Generators of sandpile groups of wheel graphs
As noted above Biggs described the structure of $W\_n$ and provided also generators in case of $n$ is odd, see Theorem 9.2 in "[Chip-Firing and the Critical Group of a Graph](https://link.springer.com/article/10.1023/A:1018611014097)". The even case is considered as well.


