Abstract:

We study the critical group of the cone over a sandwich graph. It is shown that this group can be described as the cokernel of a discrete Laplace operator. Furthermore, we prove that its exact structure can be determined by making use of a recurrence relation derived from the Laplace operator. This relation involves symmetric Laurent polynomials and provides a more efficient way to compute the group. The proposed method offers a powerful tool for analyzing invariants of graphs with complex combinatorial structure.