@article {1225,
title = {Levinson{\textquoteright}s theorem for graphs},
journal = {Journal of Mathematical Physics},
volume = {52},
year = {2011},
month = {2011/06/30},
pages = {082102},
abstract = { We prove an analog of Levinson{\textquoteright}s theorem for scattering on a weighted
(m+1)-vertex graph with a semi-infinite path attached to one of its vertices.
In particular, we show that the number of bound states in such a scattering
problem is equal to m minus half the winding number of the phase of the
reflection coefficient (where each so-called half-bound state is counted as
half a bound state).
},
doi = {10.1063/1.3622608},
url = {http://arxiv.org/abs/1103.5077v2},
author = {Andrew M. Childs and DJ Strouse}
}