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Results tagged with spectral-graph-theory
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user 13639
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
0
answers
118
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The algebraic connectivity of graphs with large isoperimetric number
Let $G = (V,E)$ be an undirected graph with maximum degree $\Delta$.
The isoperimetric number of $G$, denoted $i(G)$, is defined by
$$i(G) = \min_{|S| \leq |V|/2} \frac{e(S,\bar{S})}{|S|},$$
where $e …
- 519
0
votes
1
answer
213
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The Algebraic Connectivity vs. Isoperimetric Number
Let $d$ be a fixed number. By the Cheeger theory and theory of expanders, the second smallest eigenvalue of the Laplacian for a family of $d$-regular graphs is bounded bellow by a positive constant if …
- 519
5
votes
3
answers
2k
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Effect of different graph operations on spectrum of graph laplacian?
The algebraic connectivity of a graph G is the second-smallest eigenvalue of the Laplacian matrix of G. This eigenvalue is greater than 0 if and only if G is a connected graph. The magnitude of this v …
- 519