What are...graphs with small spectrum?

Goal. Explaining basic concepts in the intersection of graph theory and algebra in an intuitive way. This time. What are...graphs with small spectrum? Or: ADE is it! Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Disclaimer. Graph theory is one of the most applicable fields of mathematics, essentially by birth, but also a very wide area of beautiful results and active research. So to be precise, this video series is mostly about the interaction between graphs, matrices and polynomials and their various friends. That is, algebraic methods are applied to problems regarding graphs, and potentially also the other way around. Slides. http://www.dtubbenhauer.com/youtube.html Website with exercises. http://www.dtubbenhauer.com/lecture-a... Thumbnail. I only need 2cos(ipi/(n+1)) ;-) Algebraic graph theory. https://en.wikipedia.org/wiki/Algebra... https://en.wikipedia.org/wiki/Adjacen... https://en.wikipedia.org/wiki/Laplaci... https://en.wikipedia.org/wiki/Spectra... https://en.wikipedia.org/wiki/Tutte_p... https://en.wikipedia.org/wiki/Chromat... https://en.wikipedia.org/wiki/Bollob%... https://en.wikipedia.org/wiki/Graph_p... Graph theory. https://en.wikipedia.org/wiki/Graph_(...) https://en.wikipedia.org/wiki/Graph_(...) https://en.wikipedia.org/wiki/List_of... https://en.wikipedia.org/wiki/Network... https://en.wikipedia.org/wiki/Tree_(g...) https://en.wikipedia.org/wiki/Graph_c... https://en.wikipedia.org/wiki/List_of... Applications of (algebraic) graph theory. https://www.zib.de/groetschel/teachin... https://link.springer.com/book/10.100... https://link.springer.com/book/10.100... https://people.unipmn.it/fragnelli/di... https://koreascience.kr/article/JAKO2... https://math.stackexchange.com/questi... https://math.stackexchange.com/questi... https://math.stackexchange.com/questi... https://en.wikipedia.org/wiki/PageRank https://en.wikipedia.org/wiki/List_of... https://towardsdatascience.com/what-i... https://www.xomnia.com/post/graph-the... Pictures used. Pictures from https://www.win.tue.nl/~aeb/2WF05/spe... https://upload.wikimedia.org/wikipedi... More pictures from https://www.win.tue.nl/~aeb/2WF05/spe... Many more pictures from https://www.win.tue.nl/~aeb/2WF05/spe... Picture from https://www.sciencedirect.com/science... Some books I am using (I sometimes steal some pictures from there). https://www.win.tue.nl/~aeb/2WF05/spe... also: https://link.springer.com/book/10.100... https://www.math.arizona.edu/~kglasne... also: https://link.springer.com/book/10.100... https://link.springer.com/book/10.100... https://link.springer.com/book/10.100... https://www.zib.de/groetschel/teachin... also: https://link.springer.com/book/978184... https://www.cambridge.org/core/books/... https://diestel-graph-theory.com/ also: https://link.springer.com/book/10.100... Mathematica. https://reference.wolfram.com/languag... https://reference.wolfram.com/languag... https://demonstrations.wolfram.com/to... SageMath. https://doc.sagemath.org/html/en/refe... #graphtheory #algebra #mathematics