Block structures of graphs and quantum isomorphism
Combinatorics
2025-10-23 v2 Operator Algebras
Quantum Algebra
Abstract
We prove that for every pair of quantum isomorphic graphs, their block trees and their block graphs are isomorphic, and that such an isomorphism can be chosen so that the corresponding blocks are quantum isomorphic -- in particular, 2-connectedness is preserved under quantum isomorphism. We conclude with some corollaries, including obtaining some necessary conditions on a pair of quantum isomorphic, not isomorphic graphs with a minimal number of vertices.
Cite
@article{arxiv.2502.19343,
title = {Block structures of graphs and quantum isomorphism},
author = {Amaury Freslon and Paul Meunier and Pegah Pournajafi},
journal= {arXiv preprint arXiv:2502.19343},
year = {2025}
}
Comments
24 pages