TransWikia.com

Generators of sandpile groups of wheel graphs

MathOverflow Asked by castor on February 16, 2021

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.

One Answer

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.

Correct answer by castor on February 16, 2021

Add your own answers!

Ask a Question

Get help from others!

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP