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 Feb7 asked Simpler expression for binomial sum Dec15 awarded Caucus Nov17 awarded Good Question Oct24 revised Examples of sequences of graphs with different order of Cheeger constant and spectral gap Added a condition Oct23 asked Examples of sequences of graphs with different order of Cheeger constant and spectral gap Oct7 awarded Yearling Oct6 revised Are the eigenvectors of vertex transitive graphs bounded Corrected grammar Sep30 awarded Explainer Sep25 comment Are the eigenvectors of vertex transitive graphs bounded I usually don't work with the ordinary $L^2$ norm, and this was the easiest way to describe the problem with out actually defining the norm. Sep25 answered The meaning of the entries of eigenvectors of graphs Jul2 awarded Curious Apr23 comment Can a cube always be fitted into the projection of a cube? It should be centered around the origin. I edited the question so that this is clear. Apr23 revised Can a cube always be fitted into the projection of a cube? Added a restriction Apr21 comment Can a cube always be fitted into the projection of a cube? Only orthogonal I think Apr20 awarded Nice Question Apr15 comment Are the eigenvectors of vertex transitive graphs bounded Given that $\| \psi \|_2^2=|S|$, it is obvious that $\| \psi \|_\infty<\sqrt{|S|}$ for any such $\psi$. Apr15 awarded Promoter Apr14 revised Does any vertex transitive graph have a bounded eigenvector? Changed the question slightly to make it more restrictive, and hopefully easier to answer Apr12 comment Does any vertex transitive graph have a bounded eigenvector? @user126154, the property you describe is irreducibility of the random walk/Markov chain, this is NOT the same as vertex transitivity. See here: en.wikipedia.org/wiki/Vertex-transitive_graph Apr11 comment Number of Nodes within a Given Distance from a Node The book "Spectral Graph theory" by Fan Chung (the first chapters are avaiable online through her homepage) contains some such bounds, e.g. $\max_{i \not = 1} |\lambda_i| \geq \sqrt{\frac{n-d}{(n-1)d}}$.