@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} }