Geodesic
The critical groups of Adinkras up to 2-rank of Cayley graphs
Chi Ho Yuen1
1University of Oslo
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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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 Iga et al., 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.
DOI : 10.37236/11758
Classification : 05C50, 05C22, 05E30, 05C25
Mots-clés : Cayley graphs for supersymmetry algebras, monodromy pairing

Chi Ho Yuen  1

1 University of Oslo 
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Chi Ho Yuen. The critical groups of Adinkras up to 2-rank of Cayley graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/11758

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