This work extends the results of [1, 2, 3] where the Symplectic Wron-skian was constructed for the linear systems on Graphs and applied in the Scattering Theory for the Graphs with tails. Let us consider any one-dimensional locally finite simplicial complex (Graph) Γ without ends (i.e. every vertex P belongs to at least two but to the finite number of edges R i only). All set of vertices is num...

Given a finite set E, a subset D ✓ E (viewed as a function E ! F2) is orthogonal to a given subspace F of the F2-vector space of functions E ! F2 as soon as D is orthogonal to every ✓-minimal element of F . This fails in general when E is infinite. However, we prove the above statement for the six subspaces F of the edge space of any 3-connected locally finite graph that are relevant to its hom...