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Pré-Publication, Document De Travail Année : 2024

Graphs and their symmetries

Teo Banica
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Résumé

This is an introduction to graph theory, from a geometric viewpoint. A finite graph $X$ is described by its adjacency matrix $d\in M_N(0,1)$, which can be thought of as a kind of discrete Laplacian, and we first discuss the basics of graph theory, by using $d$ and linear algebra tools. Then we discuss the computation of the classical and quantum symmetry groups $G(X)\subset G^+(X)$, which must leave invariant the eigenspaces of $d$. Finally, we discuss similar questions for the quantum graphs, with these being again described by certain matrices $d\in M_N(\mathbb C)$, but in a more twisted way.
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Dates et versions

hal-04602820 , version 1 (06-06-2024)

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  • HAL Id : hal-04602820 , version 1

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Teo Banica. Graphs and their symmetries. 2024. ⟨hal-04602820⟩
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