Constructing physically intuitive graph invariants

Abstract

In this brief note I try to give a simple example of where physical intuition about a collection of interacting qubits can lead to the construction of "natural" versions of what are, generically, quite abstract mathematical objects - in this case graph invariants. This note is written primarily for physicists who do not want to go through the painful process of trying to understand Ed Witten's vastly more complicated construction of physically intuitive knot invariants, but who'd like some idea of how physical intuition can play a role in such things.

3 pages, 2 figures

Cited by in corpus (13)

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• On the Connectivity of Token Graphs of Trees
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• The quantum algorithm for graph isomorphism problem
• Hamiltonicity of the Double Vertex Graph and the Complete Double Vertex Graph of some Join Graphs
• The Edge-connectivity of Token Graphs
• A matrix representation of graphs and its spectrum as a graph invariant
• On the Laplacian spectra of token graphs
• Symmetric Squares of Graphs
• The packing number of the double vertex graph of the path graph
• Investigating graph isomorphism in cospectral graphs via multiparticle quantum walk in fermionic basis and entanglement entropy