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Results tagged with laplacian
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user 1492
The Laplacian matrix is the representation of a graph in matrix form.
4
votes
Multiplicity of the smallest non-zero Laplacian eigenvalue for tree graphs
All the Laplacian eigenvalues of the star graph $K_{1,n}$ other than $n+1$ and $0$ are equal to $1$.
Computer experimentation reveals a modest number of additional examples. …
- 12.7k
5
votes
Accepted
When do the nonzero eigenvalues of a directed graph Laplacian have the same absolute value?
This is false.
Run this code in SageMath; you can do this at sagecell.sagemath.org if you do not have SageMath already installed on your own computer.
h = DiGraph('DKCYW?')
print(h.laplacian_matrix(). …
- 12.7k
15
votes
Accepted
is it possible to have two non-isomorphic non-regular graphs with the same adjacent spectrum...
Yes, Brendan McKay showed that almost all trees have mates that are simultaneously cospectral in both adjacency and Laplacian spectra. And more. …
- 12.7k