A construction of distance cospectral graphs
A construction of distance cospectral graphs
复制标题
距离共谱图的构造
DOI：
10.1016/j.laa.2017.09.005
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Kristin Heysse
中科院分区：
文献类型：
--
作者：
Kristin Heysse
连通图的距离矩阵是对称矩阵，其列和行由顶点索引，并且元素是对应顶点之间的成对距离。我们给出了一个不同的图，在他们的边缘计数，但相对于距离矩阵的共谱的建设。此外，我们确定了一个子图切换行为，构建额外的距离共谱图。这两种构造的证明都依赖于一个图的（大部分）距离特征向量的扰动，以产生另一个图的距离特征向量。
The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in their edge counts yet are cospectral with respect to the distance matrix. Further, we identify a subgraph switching behavior which constructs additional distance cospectral graphs. The proofs for both constructions rely on a perturbation of (most of) the distance eigenvectors of one graph to yield the distance eigenvectors of the other.