  This work is the direct continuation of the author's note published in
Russian Math Surveys 52 (1997), no 6. Discrete Schrodinger operators on graphs
and higher dimensional simplicial complexes are considered. A vector-valued
symplectic form on the space of solutions is consructed. This form, "Symplectic
Wronskian", takes value in the group of 1-dimensional cycles. This construction
has important applications for the Scattering Theory on graphs with tails.
Effective diagonalization of the real Fermionic quadratic form is presented in
the Appendix. This construction appeared first time in 1987 in the author's
paper dedicated to an analogue of Morse theory for vector fields (it was
published as an Appendix to the author's joint paper with M.Shubin, Soviet Math
Dokl 34 (1987) no 1).
