Abstract
On a finite metric graph with standard vertex conditions and equal edge lengths, the large magnitude eigenvalues of the Schrodinger op- erator ∆ + q cluster near the eigenvalues of the Laplace operator ∆. Based on the spectral 'periodicity' of ∆, the clusters can be parti- tioned into a finite collection of classes. There is a class dependent formula for the cluster trace (or average eigenvalue shift) in the large magnitude limit which expresses the trace as a function of the edge integrals e q and data from the underlying combinatorial graph.
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