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Results tagged with spectral-graph-theory
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user 290
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
Spectral radius of a proper subgraph
There is a pretty straightforward counting argument which I give as Lemma 6 here. I don't think it is the standard argument, though.
- 118k
2
votes
Spectral properties of Cayley graphs
I know at least one special case where your second question makes sense. If $G$ is a compact group, it has a category $\text{Rep}(G)$ of finite-dimensional unitary representations which break up into …
- 118k
27
votes
Accepted
Factorization of the characteristic polynomial of the adjacency matrix of a graph
Expanding on Richard's comment: let me rename your graph to $S$ and consider the adjacency matrix $A$ abstractly as a linear operator acting on the free vector space $\mathbb{C}[S]$ on (the vertices o …
- 118k