Quantum isomorphic strongly regular graphs from the E₈ root system

2022/09/29 by Simon Schmidt, Schmidt, Simon · 1 citation
Chemistry · Materials Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graphene research and applications #Quantum Algebra (math.QA) #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2209.14906

openalex publication_date 2022/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

In this article, we give a first example of a pair of quantum isomorphic, non-isomorphic strongly regular graphs, that is, non-isomorphic strongly regular graphs having the same homomorphism counts from all planar graphs. The pair consists of the orthogonality graph of the 120 lines spanned by the E₈ root system and a rank 4 graph whose complement was first discovered by Brouwer, Ivanov and Klin. Both graphs are strongly regular with parameters (120, 63, 30, 36). Using Godsil-McKay switching, we obtain more quantum isomorphic, non-isomorphic strongly regular graphs with the same parameters.

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