On the sandpile model of modified wheels II
<p>We investigate the abelian sandpile group on modified wheels Ŵ<sub>n </sub>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 clas...
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| مؤلفون آخرون: | , , |
| منشور في: |
2023
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إضافة وسم
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| الملخص: | <p>We investigate the abelian sandpile group on modified wheels Ŵ<sub>n </sub>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<sub>n </sub>is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on Ŵ<sub>n </sub>is the direct product of two cyclic subgroups of order a<sub>n </sub>and 3a<sub>n </sub>for n even and of orderan a<sub>n </sub>and 2a<sub>n</sub> for n odd, respectively.</p> <h2>Other information</h2> <p>Published in: Open Mathematics<br> License: <a href="http://creativecommons.org/licenses/by/4.0" target="_blank">http://creativecommons.org/licenses/by/4.0</a><br> See article on publisher's website: <a href="http://dx.doi.org/10.1515/math-2020-0094" target="_blank">http://dx.doi.org/10.1515/math-2020-0094</a> </p> |
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