%0 Journal Article %J Journal of Mathematical Physics %D 2011 %T Levinson's theorem for graphs %A Andrew M. Childs %A DJ Strouse %X We prove an analog of Levinson'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). %B Journal of Mathematical Physics %V 52 %P 082102 %8 2011/06/30 %G eng %U http://arxiv.org/abs/1103.5077v2 %N 8 %! J. Math. Phys. %R 10.1063/1.3622608