JP Journal of Algebra, Number Theory and Applications
Volume 40, Issue 3, Pages 229 - 240
(June 2018) http://dx.doi.org/10.17654/NT040030229 |
|
ON THE SANDPILE GROUP OF A FAMILY OF GRAPHS
Zahid Raza and Sidra Iqbal
|
Abstract: The sandpile group is a subtle isomorphism invariant of a graph and is closely connected with the graph Laplacian matrix. In this paper, the abstract structure of the sandpile group of a family of graphs is determined. It is shown that the sandpile group is always isomorphic to the direct sum of two cyclic groups. |
Keywords and phrases: graph, Laplacian matrix, sandpile group, invariant factor, Smith normal form, tree number. |
|
Number of Downloads: 520 | Number of Views: 5285 |
|