论文标题
关于块图的逆特征值问题
On the inverse eigenvalue problem for block graphs
论文作者
论文摘要
图$ g $的逆特征值问题旨在找到$（i，j）$ - $ i \ neq j $的矩阵的所有可能的光谱，而当$ i $与$ j $相邻时。在这项工作中，针对集团图形的亚家族完全解决了逆特征值问题，特别是对于Lollipop图和广义杠铃图。对于带有关联的图形$ g $的矩阵$ a $，引入了一种使用强频谱属性的新技术，从而使我们可以通过附加集团在任意特征值列表中添加矩阵$ a'$从$ g $获得的矩阵$ a'$。因此，许多光谱显示用于块图。
The inverse eigenvalue problem of a graph $G$ aims to find all possible spectra for matrices whose $(i,j)$-entry, for $i\neq j$, is nonzero precisely when $i$ is adjacent to $j$. 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 $A'$ 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.
