Improved bound on the non zero eigenvalues of the graph Laplacian coming from quantum symmetry of vertex transitive graphs

2019/12/19 by Soumalya Joardar, Joardar, Soumalya
Mathematics · Physics and Astronomy · #05C50 #46L30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Graph theory and applications #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Spectral Theory in Mathematical Physics #math.QA #msc:05C50 #msc:46L30

paper · pdf · doi:10.48550/arxiv.1912.09317

11 pages

arxiv created 2019/12/19 · openalex publication_date 2019/12/19 · arxiv updated 2019/12/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

A chain of quantum subgroups of the quantum automorphism group of finite graphs has been introduced. It generalizes the construction of J. Bichon (see [3]) in a sense. A better bound of the non zero eigenvalues of the graph Laplacian has been obtained using the chain of quantum subgroups.

Citations

• Notes on Compact Quantum Groups

Related

• Eigenvalue estimates on quantum graphs
• Graphs and their symmetries
• Quantum automorphism groups of finite graphs
• Surgery transformations and eigenvalue estimates for quantum graphs with δ' vertex interactions
• A family of diameter-based eigenvalue bounds for quantum graphs