  Quantum graphs can be extended to scattering systems when they are connected
by leads to infinity. It is shown that for certain extensions, the scattering
matrices of isospectral graphs are conjugate to each other and their poles
distributions are therefore identical. The scattering matrices are studied
using a recently developed isospectral theory. At the same time, the scattering
approach offers a new insight on the mentioned isospectral construction.
