The critical groups of Adinkras up to 2-rank of Cayley graphs (Q6197813)

Summary: Adinkras are graphical gadgets introduced by physicists to study supersymmetry, which can be thought of as the Cayley graphs for supersymmetry algebras. Improving the result of \textit{K. Iga} et al. [Adv. Appl. Math. 143, Article ID 102450, 45 p. (2023; Zbl 1504.05116)], we determine the critical group of an Adinkra given the \(2\)-rank of the Laplacian of the underlying Cayley graph. As a corollary, we show that the critical group is independent of the signature of the Adinkra. The proof uses the monodromy pairing on these critical groups.