In this work, the inverse eigenvalue problem is completely solved for a subfamily of clique-path graphs, in particular for lollipop graphs and generalized barbell graphs. For a matrix A with associated graph G, a new technique utilizing the strong spectral property is introduced, allowing us to construct a matrix $A^{\prime }$ whose graph is obtained from G by appending a clique while arbitrary list of eigenvalues is added to the spectrum. Consequently, many spectra are shown realizable for block graphs.

中文翻译：

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关于块图的逆特征值问题

在这项工作中，对于集团路径图的子族，特别是棒棒糖图和广义杠铃图，完全解决了逆特征值问题。对于具有关联图G的矩阵A，引入了一种利用强谱属性的新技术，允许我们构造矩阵${\mathrm{一种}}^{\prime }$其图是通过附加一个团从G获得的，同时将任意特征值列表添加到频谱中。因此，许多光谱显示为块状图是可实现的。