Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition

In this paper, we develop two approaches to investigation of inverse spectral problems for a new class nonlocal operators on metric graphs. The Laplace differential operator is considered star-shaped graph with integral matching condition. This adjoint the functional-differential frozen argument at central vertex graph. We study problem that consists in recovery condition coefficients from eigenvalues. obtain spectrum characterization, reconstruction algorithms, and prove uniqueness solution.