Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Levinson's theorem for graphs II   We prove Levinson's theorem for scattering on an (m+n)-vertex graph with n
semi-infinite paths each attached to a different vertex, generalizing a
previous result for the case n=1. This theorem counts the number of bound
states in terms of the winding of the determinant of the S-matrix. We also
provide a proof that the bound states and incoming scattering states of the
Hamiltonian together form a complete basis for the Hilbert space, generalizing
another result for the case n=1.

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph