The generalized distance matrix of a graph is the matrix whose entries depend only on the pairwise distances between vertices, and the generalized distance spectrum is the set of eigenvalues of this matrix. This framework generalizes many of the commonly studied spectra of graphs. We show that for a large class of graphs these eigenvalues can be computed explicitly. We also present the applications of our results to competition models in ecology and rapidly mixing Markov chains.

中文翻译：

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图的广义距离谱及其应用

图的广义距离矩阵是其条目仅取决于顶点之间的成对距离的矩阵，而广义距离谱是该矩阵的特征值集。该框架概括了许多常用的图谱。我们表明，对于一大类图，这些特征值可以显式计算。我们还介绍了我们的结果在生态学和快速混合马尔可夫链的竞争模型中的应用。