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Results tagged with expander-graphs
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user 4558
An expander graph is a graph in which small sets of vertices have large 'boundary'. Ramanujan graphs are examples of expanders.
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Ramanujan graphs from varieties over finite fields
Let $G$ be a $d$-regular graph. Let $d= \lambda_1 \ge \lambda_2 \ge \dots \ge \lambda_n \ge -d $ be the eigenvalues of the adjacency matrix of $G$, and set $\lambda = \max (|\lambda_2| , |\lambda_n|) …
- 7,857
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What are the best bounds to date on the maximum girth of a cubic graph?
The girth of a graph is the length of its smallest cycle. Studying the maximum possible girth for a $k$-regular graph on $n$ vertices is a very well-studied problem.
In the 1988 paper "Ramanujan grap …
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Ramanujan graphs from varieties over finite fields
Someone pointed me to a reference that answers my question about whether this example is new, so I will answer my own question in case it is helpful for anyone else.
This paper:
https://dl.acm.org/doi …
- 7,857
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Do there exist "expanding" $1$-skeletons of simple $4$-polytopes?
Let $\{ G_n \}_{n \ge 1}$ be a sequence of graphs such that the number of vertices of $G_n$ tends to $\infty$ as $n \to \infty$. We say that $\{ G_n \}_{n \ge 1}$ is an expander family if
$\lambda_2( …
- 7,857