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Rodrigo de Azevedo
Rodrigo de Azevedo
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spectrum Spectrum of an adjacency matrix

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Delio Mugnolo
Delio Mugnolo
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Spectrum spectrum of an adjacency matrix

The adjacency matrix of a non-oriented connected graph is symmetric. Hence, hence its spectrum is real.

If the graph is bipartite, then the spectrum of its adjacency matrix is symmetric about $0$0. A few lower bounds on the smallest eigenvalue are known in the literature, but I could not find any upper bound. Hence my question: What is known about this? Do there exist graphs whose adjacency matrix is positive semidefinitesemi-definite?

Spectrum of an adjacency matrix

The adjacency matrix of a non-oriented connected graph is symmetric. Hence, its spectrum is real.

If the graph is bipartite, then the spectrum of its adjacency matrix is symmetric about $0$. A few lower bounds on the smallest eigenvalue are known in the literature, but I could not find any upper bound. Hence my question: What is known about this? Do there exist graphs whose adjacency matrix is positive semidefinite?

spectrum of an adjacency matrix

The adjacency matrix of a non-oriented connected graph is symmetric, hence its spectrum is real.

If the graph is bipartite, then the spectrum of its adjacency matrix is symmetric about 0. A few lower bounds on the smallest eigenvalue are known in the literature, but I could not find any upper bound. Hence my question: What is known about this? Do there exist graphs whose adjacency matrix is positive semi-definite?

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edit approved Aug 19, 2017 at 16:36
Rodrigo de Azevedo
edit approved Aug 19, 2017 at 16:36
Rodrigo de Azevedo
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spectrum Spectrum of an adjacency matrix

The adjacency matrix of a non-oriented connected graph is symmetric. Hence, hence its spectrum is real.

If the graph is bipartite, then the spectrum of its adjacency matrix is symmetric about 0$0$. A few lower bounds on the smallest eigenvalue are known in the literature, but I could not find any upper bound. Hence my question: What is known about this? Do there exist graphs whose adjacency matrix is positive semi-definitesemidefinite?

spectrum of an adjacency matrix

The adjacency matrix of a non-oriented connected graph is symmetric, hence its spectrum is real.

If the graph is bipartite, then the spectrum of its adjacency matrix is symmetric about 0. A few lower bounds on the smallest eigenvalue are known in the literature, but I could not find any upper bound. Hence my question: What is known about this? Do there exist graphs whose adjacency matrix is positive semi-definite?

Spectrum of an adjacency matrix

The adjacency matrix of a non-oriented connected graph is symmetric. Hence, its spectrum is real.

If the graph is bipartite, then the spectrum of its adjacency matrix is symmetric about $0$. A few lower bounds on the smallest eigenvalue are known in the literature, but I could not find any upper bound. Hence my question: What is known about this? Do there exist graphs whose adjacency matrix is positive semidefinite?

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Delio Mugnolo
Delio Mugnolo
  • 3.4k
  • 21
  • 42
Source Link
Delio Mugnolo
Delio Mugnolo
  • 3.4k
  • 21
  • 42