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Results tagged with spectral-graph-theory
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user 125498
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
3
votes
Upper bounds for the second largest eigenvalue in terms of degree?
There exists arbitrarily large $d$-regular graphs with a cut edge. A direct inspection shows that the expansion tends to $0$. By the Cheeger inequality, $λ_2$ is arbitrarily close to $d=λ_1$.
There c …
- 9,501
8
votes
Accepted
Are there graphs with irrational eigenvalues which are all $>1$?
Yes, the graph with adjacency matrix
0 0 1 0 1 1 1 1
0 0 0 1 0 0 0 1
1 0 0 0 1 1 1 1
0 1 0 0 0 …
- 9,501
4
votes
Accepted
Strongly/distance regular graphs over $\mathbb{Z}_2^n$ with the same parameters
The answer is yes.
There are many difference sets on the group $\mathbb Z_2^6$, which can be found in the La Jolla repository.
Below is the SageMath code to generate two nonisomorphic $\mathbb Z_2^6$- …
- 9,501
8
votes
Accepted
Graph embeddings in the projective plane: for the 35 forbidden minors, do we know their Coli...
Here's a table containing the Colin de Verdière numbers:
Name Graph6 μ Reason
K33 + K33 4 (components linklessly embeddable)
K5 + K33 4 (components linkl …
- 9,501