The Critical Groups of the Peisert Graphs
نویسنده
چکیده
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 p2 with p ≡ 3 (mod 4) are similar over the `-local integers for every prime `. 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.
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