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Results tagged with spectral-graph-theory
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user 175976
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
6
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Relationship between spectral gaps of adjacency and Laplacian matrices of graphs
Let $G$ be an undirected simple graph on $n$ vertices, with self-loops allowed, and with arbitrary positive edge weights $w_{u,v}$ (which is $0$ if there is no edge between $u$ and $v$).
Let $A$ be th …
- 150
3
votes
Accepted
Relationship between spectral gaps of adjacency and Laplacian matrices of graphs
Well, I found a counterexample (actually, many) to this claim. In fact, it only has 7 vertices: it is given by the graph6 string "F{O_w". Here's a picture:
Now the question becomes whether there is a …
- 150