TY - JOUR T1 - Levinson's theorem for graphs JF - Journal of Mathematical Physics Y1 - 2011 A1 - Andrew M. Childs A1 - DJ Strouse AB - 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). VL - 52 U4 - 082102 UR - http://arxiv.org/abs/1103.5077v2 CP - 8 J1 - J. Math. Phys. U5 - 10.1063/1.3622608 ER -