A modified local Weyl law and spectral comparison results for <i>δ</i>′-coupling conditions

We study Schrödinger operators on compact finite metric graphs subject to δ′-coupling conditions. Based on a novel modified local Weyl law, we derive an explicit expression for the limiting mean eigenvalue distance of two different self-adjoint realisations on a given graph. Furthermore, using this spectral comparison result, we also study the limiting mean eigenvalue distance comparing δ′-coupling conditions to so-called anti-Kirchhoff conditions, showing divergence and thereby confirming a numerical observation in Band, Schanz, and Sofer [Ann. Henri Poincaré 25, 3859–3898 (2024)].