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

TL;DR

This paper introduces a new bound on the non-zero eigenvalues of the graph Laplacian by leveraging the quantum symmetry properties of vertex transitive graphs, extending previous quantum automorphism group work.

Contribution

It provides an improved eigenvalue bound for graph Laplacians using a novel chain of quantum subgroups related to quantum automorphism groups.

Findings

Established a new bound on non-zero eigenvalues of graph Laplacian

Generalized Bichon's construction of quantum automorphism groups

Enhanced understanding of quantum symmetries in vertex transitive graphs

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.