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Inverse nodal problems for Sturm–Liouville equations on graphs

We consider inverse nodal problems on graphs. Eigenfunction and eigenvalue asymptotic approximations are used to provide an asymptotic expression for the spacing of nodal points on each edge of the graph. Based on this, the uniqueness of the potential for given nodal data is proved and we give a construction of q as a limit, in , of a sequence of functions whose nth term is dependent only on the nth eigenvalue and its associated nodal data.