The indefinite Kirchhoff Laplacian on a unit-star graph has spectrum {±(kπ)^2 with multiplicities n_±−1} plus simple eigenvalues η_k, and is similar to a self-adjoint operator.
Introduction to quantum graphs , vol
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1-D Schr\"odinger operator on a star graph with nondefinite weight function
The indefinite Kirchhoff Laplacian on a unit-star graph has spectrum {±(kπ)^2 with multiplicities n_±−1} plus simple eigenvalues η_k, and is similar to a self-adjoint operator.