The paper is a continuation of the study started in \cite{Yorzh1}.
Schrodinger operators on finite compact metric graphs are considered under the
assumption that the matching conditions at the graph vertices are of δ
type. Either an infinite series of trace formulae (provided that edge
potentials are infinitely smooth) or a finite number of such formulae (in the
cases of L1​ and CM edge potentials) are obtained which link together two
different quantum graphs under the assumption that their spectra coincide.
Applications are given to the problem of recovering matching conditions for a
quantum graph based on its spectrum.Comment: arXiv admin note: substantial text overlap with arXiv:1403.761