1-D Schrödinger operator on a star graph withnondefinite weight function

We investigate the indefinite Kirchhoff Laplacian on a star graph G with n = n+ + n− edges of unit length, where the differential operator acts as minus second derivative on n_+ edges and plus second derivative on n_− edges. The operator is subject to Dirichlet conditions at the outer vertices and Kirchhoff conditions at the central vertex. We establish that this operator is similar to a self-adjoint operator in the Hilbert space L^2(G) and that its eigenfunctions constitute a Riesz basis. Additionally, we provide a complete characterization of its point spectrum