Eigenvalues and critical groups of Adinkras

Kevin Iga, Caroline Klivans*, Jordan Kostiuk, Chi Ho Yuen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Adinkras are signed graphs used to study supersymmetry in physics. We provide an introduction to these objects, and study the properties of their signed adjacency and signed Laplacian matrices. These matrices each have exactly two distinct eigenvalues (of equal multiplicity), making Adinkras closely related to the notions of strongly regular graphs. We also study the critical groups of Adinkras, and in particular determine their odd components. A novel technique of independent interest is used which considers modules over polynomial rings in order to study critical groups as Z-modules.

Original languageEnglish
Article number102450
JournalAdvances in Applied Mathematics
StatePublished - Feb 2023


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