LAUSR

The critical group of a finite graph is an abelian group defined by the Smith normal form of the Laplacian. We determine the critical groups of the Peisert graphs, a certain family of strongly regular graphs similar to, but different from, the Paley graphs. It is further shown that the adjacency matrices of the two graphs defined over a field of order $$p^2$$p2 with $$p\equiv 3\pmod 4$$p≡3(mod4) are similar over the $$\ell $$ℓ-local integers for every prime $$\ell $$ℓ. Consequently, each such pair of graphs provides an example where all the corresponding generalized adjacency matrices are both cospectral and equivalent in the sense of Smith normal form.