Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertibility of graph translation and support of Laplacian Fiedler
  vectors   The graph Laplacian operator is widely studied in spectral graph theory
largely due to its importance in modern data analysis. Recently, the Fourier
transform and other time-frequency operators have been defined on graphs using
Laplacian eigenvalues and eigenvectors. We extend these results and prove that
the translation operator to the $i$'th node is invertible if and only if all
eigenvectors are nonzero on the $i$'th node. Because of this dependency on the
support of eigenvectors we study the characteristic set of Laplacian
eigenvectors. We prove that the Fiedler vector of a planar graph cannot vanish
on large neighborhoods and then explicitly construct a family of non-planar
graphs that do exhibit this property.

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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th