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Results tagged with spectral-graph-theory
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user 2233
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
2
votes
Accepted
In what probability does cospectra of Cayley graph imply isomorphism of the corresponding group
For your second question, if by probability you mean $$\lim_{n \to \infty} \frac{|S_n|}{|G_n|},$$ where $S_n$ is the set of all possible spectra of simple $n$-vertex graphs, and $G_n$ is the set of is …
- 32.1k
4
votes
Accepted
Cocktail party and tripartite graphs are DS?
Yes, the cocktail party graphs and $K_{n,n,n}$ are determined by the spectra of their adjacency matrix. See for example, Proposition 6 of the paper Which graphs are determined by their spectrum? by v …
- 32.1k
5
votes
Is there a continuous analogue of Ramanujan graphs?
One possible answer can be found in the theory of graph limits, where large graphs are modelled by continuous objects. In particular, a graphing is one type of continuous analogue of a graph, and it …
- 32.1k
2
votes
Lovasz theta function - uses
One of the most important properties of the Lovász theta function is that for any $\epsilon >0$, it can be approximated to within an $\epsilon$ additive error in polynomial time (by the Ellipsoid Meth …
12
votes
Classes of graphs for which isospectrum implies isomorphism?
It is conjectured that almost all graphs are determined by their spectrum. It is funny that this conjecture fails spectacularly for many classes of graphs that one can think of. For example, almost …
- 32.1k