Connectivity preservation under quantum isomorphism

Determine whether there exists a pair of quantum-isomorphic graphs whose vertex connectivities are different.

Background

The main results prove that 2-connectedness is preserved under quantum isomorphism and establish corresponding preservation results for block structures. The authors ask whether this preservation extends to the numerical connectivity of graphs. A positive answer would distinguish quantum isomorphism from ordinary cospectrality, since cospectral graphs can have different connectivities.