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Results tagged with spectral-graph-theory
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user 18606
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
5
votes
A graph spectra problem?
The adjacency matrix of the product is $A_1 \otimes J + I \otimes A_2$, where $J$ is the all ones matrix of size $n = |V(G_2)|$ and $I$ is the identity matrix of size $m = |V(G_1)|$. The two matrices …
- 2,339
2
votes
Accepted
Co-spectral fractional isomorphic graphs with different Laplacian spectrum
EDIT: According to your link, if two graphs are cospectral with a common equitable partition, then they have cospectral complements. But this implies that they have cospectral Seidel matrices (see The …
- 2,339
9
votes
Spectrum of orthogonality graph (2)
If $G$ is a Cayley graph for $\mathbb{Z}_2^n$ with connection set $C \subseteq \mathbb{Z}_2^n \setminus \{0\}$, then for each element $a \in \mathbb{Z}_2^n$ there is an eigenvector $v$ given by
$$v_x …
- 2,339
4
votes
How do eigenvalues of combinatorial Laplacian relates to automorphisms in graphs?
I think you can more or less only go in one direction here: a large amount of symmetry can imply few eigenvalues. Intuitively, this makes sense because if $f: V(G) \to \mathbb{R}$ is an eigenvector fo …
- 2,339