An optimization problem for ${\delta }^{\mathrm{\prime }}$ leaky stars

We consider singular Schrödinger operators with an attractive ${\delta }^{\mathrm{\prime }}$ interaction of strength $\beta$ supported by a star graph and prove that the ground-state eigenvalue is uniquely maximized by stars of the maximum symmetry. Two different proofs are presented, one for an even number of edges using a comparison to the $\delta$ interaction star, the other general based on Birman-Schwinger technique.