Graphs and their symmetries
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913558737977344 |
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| author | Banica, Teo |
| author_facet | Banica, Teo |
| contents | This is an introduction to graph theory, from a geometric and analytic viewpoint. A finite graph $X$ is described by its adjacency matrix $d\in M_N(0,1)$, 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 $G(X)\subset G^+(X)$, which must leave invariant the eigenspaces of $d$, with the quantum symmetry group $G^+(X)$ being in general bigger than the classical symmetry group $G(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graphs and their symmetries Banica, Teo Quantum Algebra Mathematical Physics Combinatorics Operator Algebras This is an introduction to graph theory, from a geometric and analytic viewpoint. A finite graph $X$ is described by its adjacency matrix $d\in M_N(0,1)$, 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 $G(X)\subset G^+(X)$, which must leave invariant the eigenspaces of $d$, with the quantum symmetry group $G^+(X)$ being in general bigger than the classical symmetry group $G(X)$. |
| title | Graphs and their symmetries |
| topic | Quantum Algebra Mathematical Physics Combinatorics Operator Algebras |
| url | https://arxiv.org/abs/2406.03664 |