论文标题
图形所描述的空心矩阵的逆特征值和相关问题
Inverse eigenvalue and related problems for hollow matrices described by graphs
论文作者
论文摘要
图$ g $描述的空心矩阵是一个真正的对称矩阵，其所有对角线条目等于零，并且由$ g $的邻接所管辖的偏高条目。对于给定的图$ g $，确定与$ g $相关的所有可能的矩阵光谱是$ g $的空心反向特征值问题。提出了针对路径和完整二分图的空心逆特征值问题的解决方案。相关子问题（例如可能有序的多重性列表，特征值的最大多重性和最小数量的不同特征值）的结果显示了其他图形系族。
A hollow matrix described by a graph $G$ is a real symmetric matrix having all diagonal entries equal to zero and with the off-diagonal entries governed by the adjacencies in $G$. For a given graph $G$, the determination of all possible spectra of matrices associated with $G$ is the hollow inverse eigenvalue problem for $G$. Solutions to the hollow inverse eigenvalue problems for paths and complete bipartite graphs are presented. Results for related subproblems such as possible ordered multiplicity lists, maximum multiplicity of an eigenvalue, and minimum number of distinct eigenvalues are presented for additional families of graphs.
