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Results tagged with spectral-graph-theory
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user 8799
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
0
votes
Minimum negative eigenvalue of zero-one matrices
I wish to discuss or clarify here the answers given previously.
Christian's answer fails to work for non-symmetric matrices, because then the inequality $\lambda_+\ge\frac Nn$ is deadly false. Take f …
- 52.3k
15
votes
Accepted
Eigenvalues of the complement of a graph
Edit (bis). There are two answers, depending on whether loops about vertices are allowed or not. In addition, the case of regular graphs is completely described.
If loops are allowed
The relation be …
- 52.3k
9
votes
Accepted
Are there good ways of relating a minor to the full determinant?
yes, there is the Sherman-Morrison formula
$$\det B=(\det A)(b-yA^{-1}x),$$
where $b, x$ and $y$ are blocks:
$$B=\begin{pmatrix} A & x \\ y & b \end{pmatrix}.$$
Edit. After Hachino's comment, one can …
- 52.3k