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We extend the surgical tool box for quantum graphs to anti-standard and$\delta'$ vertex conditions. Monotonicity properties of eigenvalues of graphLaplacian with $\delta'$ interactions at vertices depend on the sign of vertexparameter. Using several interlacing inequalities between eigenvalues of graphLaplacian with different vertex conditions and surgery principles we obtain newupper and lower bounds on the eigenvalues of $\delta$ and $\delta'$ Laplacians.

Surgery transformations and eigenvalue estimates for quantum graphs with $\delta'$ vertex interactions