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Eigenvectors of regular graph are annihilated by matrix of $1$s

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#linear-algebra #matrices #graph-theory #algebraic-graph-theory #spectral-graph-theory
78
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Do strongly regular graphs maximize spectral gaps?

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#algebraic-graph-theory #spectral-graph-theory #extremal-graph-theory
522
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Almost all trees are cospectral (Allen Schwenk's 1973 article)

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#graph-theory #generating-functions #trees #spectral-graph-theory #programming
458
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Characteristic polynomial of a tree

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#graph-theory #determinant #trees #spectral-graph-theory
59
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Spectral analysis

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#graph-theory #spectral-graph-theory
363
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Graphs with rational eigenvalues

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#graph-theory #eigenvalues-eigenvectors #spectral-graph-theory #adjacency-matrix
878
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Graphs with zero eigenvalues

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#graph-theory #spectral-graph-theory #adjacency-matrix
58
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Change to spectral radius due to removal of a single vertex from graph

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#graph-theory #eigenvalues-eigenvectors #algebraic-graph-theory #spectral-graph-theory #spectral-radius
518
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Small diameter, mixing time, and Expander graphs

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#combinatorics #graph-theory #markov-chains #geometric-group-theory #spectral-graph-theory
1.5k
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Show that the largest eigenvalue of a graph is strictly larger than the largest eigenvalue of any subgraph

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#graph-theory #algebraic-graph-theory #spectral-graph-theory
556
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Eigenvalues of path graph $P_n$ from eigenvalues of a cycle graph $C_{2n}$

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#linear-algebra #graph-theory #spectral-graph-theory
776
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When do the eigenvectors of a Laplacian matrix form a basis?

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#linear-algebra #eigenvalues-eigenvectors #laplacian #spectral-graph-theory #graph-laplacian
806
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Are there any positive definite adjacency matrices?

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#graph-theory #positive-definite #spectral-graph-theory
73
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Spectral gap of Cayley graph of $S_n$ with transpositions is $2/n$.

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#graph-theory #eigenvalues-eigenvectors #spectral-graph-theory
2.1k
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Spectra of adjacency matrices of bipartite graphs

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#graph-theory #reference-request #spectral-graph-theory

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