On the sandpile model of modified wheels II

We investigate the abelian sandpile group on modified wheels Ŵ_n by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45]. The complete structure of the sandpile group on a class of graphs is given in this paper. In particular, it is shown that the sandpile group on Ŵ_n is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on Ŵ_n is the direct product of two cyclic subgroups of order a_n and 3a_n for n even and of orderan a_n and 2a_n for n odd, respectively.

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Published in: Open Mathematics
License: http://creativecommons.org/licenses/by/4.0
See article on publisher's website: http://dx.doi.org/10.1515/math-2020-0094