TY - JOUR T1 - Levinson's theorem for graphs II JF - Journal of Mathematical Physics Y1 - 2012 A1 - Andrew M. Childs A1 - David Gosset AB - 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. VL - 53 U4 - 102207 UR - http://arxiv.org/abs/1203.6557v2 CP - 10 J1 - J. Math. Phys. U5 - 10.1063/1.4757665 ER -