| Autor: |
Raza Zahid, Jaradat Mohammed M. M., Bataineh Mohammed S., Ullah Faiz |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
|
| Zdroj: |
Open Mathematics, Vol 18, Iss 1, Pp 1531-1539 (2020) |
| Druh dokumentu: |
article |
| ISSN: |
2391-5455 |
| DOI: |
10.1515/math-2020-0094 |
| Popis: |
We investigate the abelian sandpile group on modified wheels Wˆn{\hat{W}}_{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 Wˆn{\hat{W}}_{n} is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on Wˆn{\hat{W}}_{n} is the direct product of two cyclic subgroups of order an{a}_{n} and 3an3{a}_{n} for n even and of order an{a}_{n} and 2an2{a}_{n} for n odd, respectively. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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