Quantum isomorphism of $2$-graphs

Abstract

We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not quantum isomorphic to each other.

26 PAGES. This is an improved version of our previous article, which now includes a new section. This addition significantly enhances the article, and therefore, Jitender Sharma's contribution is recognized with the addition of a third author. To appear in International Journal Of Mathematics