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Results tagged with spectral-graph-theory
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user 62709
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
4
votes
How networks with high largest eigenvalues are more robust?
The following papers might contain relevant information to your question:
Robustness of networks against viruses: the role of the spectral radius, by
A. Jamakovic, R.E. Kooij, P. Van Mieghem, E.R. va …
- 441
7
votes
What is a "Ramanujan Graph"?
I meant to write this as a comment to Alain's answer, but it didn't fit.
I will discuss this in terms of the eigenvalues of the adjacency matrix.
As Alain wrote, the original definition of Lubotzky …
- 441
13
votes
Do perfect matching(s) have signatures in the graph eigenvalues?
Blazsik, Cummings and Haemers http://arxiv.org/abs/1409.0630 recently constructed two regular cospectral graphs such that one has a perfect matching and the other does not.
- 441
2
votes
About distinct eigenvalues of a graph
Please see Proposition 1.3.3 in Brouwer-Haemers book available here:
http://homepages.cwi.nl/~aeb/math/ipm/
Let $\Gamma$ be a connected graph with diameter $d$. Then $\Gamma$ has at least $d+1$ dist …
- 441
1
vote
Constructing Ramanujan graphs from elliptic curves
The papers "Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?" by David Jao, Stephen D. Miller, Ramarathnam Venkatesan http://arxiv.org/abs/math/0411378 and "Expander …
- 441
10
votes
Accepted
When are (Abelian) Cayley graphs also expanders?
To add to Anthony's comment, one can make an explicit connection between the large number of walks between vertices and the spectra of Abelian Cayley graphs. It turns out that constant-degree Abelian …
- 441