Graphs and their symmetries

2024/06/06 by Banica, Teo
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2406.03664

Abstract

This is an introduction to graph theory, from a geometric and analytic viewpoint. A finite graph X is described by its adjacency matrix d∈ M_N(0,1), which can be thought of as being a kind of discrete Laplacian, and we first discuss the basics of graph theory, by using d, and various linear algebra tools. Then we discuss the computation of the classical and quantum symmetry groups G(X)⊂ G⁺(X), which must leave invariant the eigenspaces of d, with the quantum symmetry group G⁺(X) being in general bigger than the classical symmetry group G(X).

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