Constructing physically intuitive graph invariants

TL;DR

This paper illustrates how physical intuition about interacting qubits can guide the construction of natural and intuitive graph invariants, making abstract mathematical concepts more accessible to physicists.

Contribution

It provides a simple example of deriving graph invariants from physical principles, bridging physics and graph theory in an accessible way.

Findings

Physical intuition aids in constructing graph invariants.

Simplifies understanding of complex mathematical objects.

Connects quantum physics concepts with graph theory.

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.