Combinatorics and Graph Theory

    

Graphs and Their Symmetries

Authors: Teo Banica

This is an introduction to graph theory, from a geometric viewpoint. A finite graph $X$ is described by its adjacency matrix $din M_N(0,1)$, 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 $din M_N(mathbb C)$, but in a more twisted way.

Comments: 400 Pages.

Download: PDF

Submission history

[v1] 2024-06-06 00:49:05

Unique-IP document downloads: 560 times

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