We introduce Dirac-type operators with a global constant delay on a star graph consisting of m equal edges. For our introduced operators, we formulate an inverse spectral problem that is recovering the potentials from the spectra of two boundary value problems on the graph with a common set of boundary conditions at all boundary vertices except for a specific boundary vertex \(v_{0}\) (called the root). For simplicity, we restrict ourselves to the constant delay not less than the edge length of the graph. Under the assumption that the common boundary conditions are of the Robin type and they are known and pairwise linearly independent, the uniqueness theorem is proven and a constructive procedure for solving the proposed inverse problem is obtained.

我们在由m 个相等边组成的星图上引入具有全局恒定延迟的狄拉克型算子。对于我们引入的算子，我们制定了一个逆谱问题，该问题从图上的两个边值问题的谱中恢复势，在除特定边界顶点之外的所有边界顶点处具有一组公共边界条件\(v_{0} \)（称为根）。为了简单起见，我们将自己限制为不小于图的边长的恒定延迟。假设公共边界条件是Robin类型并且它们是已知的且成对线性无关，证明了唯一性定理并获得了解决所提出的反问题的构造性过程。