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On the sandpile model of modified wheels II

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submitted on 2023-03-15, 11:50 and posted on 2023-07-12, 10:00 authored by Zahid Raza, Mohammed M. M. Jaradat, Mohammed S. Bataineh, Faiz Ullah

We investigate the abelian sandpile group on modified wheels Ŵn 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 Ŵn is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on Ŵn is the direct product of two cyclic subgroups of order an and 3an for n even and of orderan an and 2an 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 

History

Language

  • English

Publisher

DeGruyter

Publication Year

  • 2020

Institution affiliated with

  • Qatar University

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