Quantum isomorphism of $2$-graphs
Soumalya Joardar, Atibur Rahaman, Jitender Sharma
TL;DR
This paper introduces the concept of quantum automorphism groups for 2-graphs, defines quantum isomorphism between them, and provides an example of two 2-graphs that are not quantum isomorphic, advancing understanding in quantum graph theory.
Contribution
It formulates quantum automorphism groups for 2-graphs, defines quantum isomorphism, and presents the first non-trivial example of non-isomorphic quantum 2-graphs.
Findings
Defined quantum automorphism groups for 2-graphs
Introduced quantum isomorphism between 2-graphs
Provided a non-trivial example of non-quantum-isomorphic 2-graphs
Abstract
We formulate a notion of the quantum automorphism group of a -graph. After some preliminary computations, we define quantum isomorphism between a pair of -graphs. We produce a `non-trivial' example of a pair of -graphs that are not quantum isomorphic to each other.
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Taxonomy
TopicsAdvanced Algebra and Logic · Algebraic structures and combinatorial models · Advanced Topics in Algebra