On the sandpile model of modified wheels II
| Author | Raza, Zahid |
| Author | Jaradat, Mohammed M. M. |
| Author | Bataineh, Mohammed S. |
| Author | Faiz Ullah |
| Available date | 2023-11-09T05:37:21Z |
| Publication Date | 2020 |
| Publication Name | Open Mathematics |
| Resource | Scopus |
| ISSN | 23915455 |
| Abstract | : We investigate the abelian sandpile group on modified wheels Wˆn 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 Wˆn is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on Wˆn is the direct product of two cyclic subgroups of order an and 3an for n even and of order an and 2an for n odd, respectively. |
| Sponsor | Open Access funding was provided by the Qatar National Library. The authors are indebted to the anonymous referees for their valuable comments to improve the original version of this paper. Zahid Raza was supported by University of Sharjah under the grant number 1802144068 and MASEP research group. |
| Language | en |
| Publisher | De Gruyter Open Ltd |
| Subject | abelian sandpile group critical configuration dollar game modified wheels stable configuration |
| Type | Article |
| Pagination | 1531-1539 |
| Issue Number | 1 |
| Volume Number | 18 |
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Materials Science & Technology [291 items ]