# Generators of sandpile groups of wheel graphs

In the paper "On the Sandpile Group of a Graph" 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" provides generators as well.

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". The even case is considered as well.