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Results tagged with spectral-graph-theory
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user 85349
Questions related to the spectrum of graphs, defined using one of the possible variants of the discrete Laplace operator or Laplacian matrix. See https://en.wikipedia.org/wiki/Discrete_Laplace_operator
6
votes
Accepted
Spectral theory of graph Laplacian besides $\lambda_2$
I came across some exciting references to 'holistic spectral data' while watching this great talk by prof. James Lee at UWashington, so it might be worth giving a look. The slides are here. A little s …
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1
vote
Accepted
Graph spectra and topology
To push this in a different direction from the comments, in the past years there have been some developments in spectral graph theory related to covering maps of graphs. Notice that this is the same n …
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5
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Behaviour of eigenspaces of adjacency matrices after a single change to the graph
What I'm about to say applies to the eigenvalues (at least). Here's what comes to my mind - it sprung from memory of some results of Batson, Spielman and Srivastava, mostly the paper "Twice Ramanujan …
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Graph lifts and representation theory
One other thing to be aware of is that since every connected even-degree regular graph is a Schreier coset graph for some group [1], we can reason about a graph in terms of the corresponding permutati …
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4
votes
0
answers
726
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Counting loops in degree: 1 or 2?
Here's what seems to be an annoying technicality when dealing with loops in graphs.
In the literature on expander graphs (and surely not only), it seems to be the convention that a loop at vertex $v$ …
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3
votes
0
answers
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Analogues of relative property $(\tau)$ for Schreier graphs
Suppose I have an expanding family of Schreier graphs $Z_n=\text{Sch}(G_n,S_n,X_n)$ of groups $G_n=\underbrace{G\wr\ldots\wr G}_{\text{$n$ times}}$ acting on sets $S_n=S^n$ by generating sets $X_n$, s …
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