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Results tagged with spectral-graph-theory
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user 19885
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
votes
An algebraic graph theory problem?
If I understood correctly, you do not have any information about $S$. In general, the answer to your question is no. The group $Z_2^n$ is not $Cay-DS$ in general. So, for suitable $n$, you can find tw …
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1
vote
Largest eigenvalue adjacency matrix-link deletion
I write this as an answer since I need some vote to break the symmetry of my reputation. I hope I never fall down to the other symmetry.
The answer of your question is yes. Actually you can see the P …
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4
votes
Accepted
normalized laplacian spectrum of trees
It is a partial answer for your question:
For $P_n$, the form of normalized laplacian matrix is three diagonal and with some calculations, we can show that all its normalized laplacian eigenvalues ar …
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2
votes
Reflexive (hyperbolic) graphs
I think this question is so hard, since we do not have any control on other eigenvalues, specially on the minimum of them.
As an evidence (and maybe useful for your work), recently S. M. Cioab$\br …
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4
votes
How networks with high largest eigenvalues are more robust?
As @Morris answered the reason is behind in connectivity and rapid connection which is compacted in isoperimetric parameter of graphs. The isoperimetric parameter has bounded by eigenvalues in some ni …
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1
vote
Cospectrality and dimension of graphs
I found the answers of the questions $(1)$ and $(2)$ and also an approach for the the third question. Also, I will introduce a software such that it is very good for finding the dimension of arbitrary …
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2
votes
Integral roots of circulant matrix
There are some good classification of Integral Cayley graphs, which by your terminology means all their adjacency matrix eigenvalues are integer. The adjacency matrices of Cayley graphs over cyclic gr …
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1
vote
Spectral radius of perturbed bipartite graphs
There are a lot of work in this direction. For an updated (and also very interesting) book, you can see:
"inequalities for graph eigenvalues" by Zoran Stanić.
Especially, you can see the chapter two …
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1
vote
Accepted
best known bounds for spectral radius
Actually you asked right question, but it is so vague to answer. Fortunately, there is a good book which you can find it very interesting. The book is:
"Spectral Radius of Graphs" by Dragan Stevanovi …
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1
vote
Spectral properties of Cayley graphs
Just for other reference, we showed that a finite DS group is solvable, and every non-cyclic Sylow subgroup of a finite DS group is of order $4$, $8$, $16$ or $9$. You can find more results in the bel …
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