Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral gap for quantum graphs and their connectivity   The spectral gap for Laplace operators on metric graphs is investigated in
relation to graph's connectivity, in particular what happens if an edge is
added to (or deleted from) a graph. It is shown that in contrast to discrete
graphs connection between the connectivity and the spectral gap is not
one-to-one. The size of the spectral gap depends not only on the topology of
the metric graph but on its geometric properties as well. It is shown that
adding sufficiently large edges as well as cutting away sufficiently small
edges leads to a decrease of the spectral gap. Corresponding explicit criteria
are given.

15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org