图的距离谱与距离（无符号）Laplacian谱是当前代数图论领域的一个重要研究内容。本项目计划研究图的距离谱与距离（无符号）Laplacian谱理论的相关问题，主要包括进一步探究连通图的距离特征值（特别是第二大距离特征值和最小距离特征值）的性质，以及某些特殊图类或给定参数（即图不变量）的连通图的距离（无符号）Laplacian谱半径取得上界的极图刻画，并考察图的距离谱展与距离无符号Laplacian谱展的相关性质。

The study of distance and distance (signless) Laplacian spectra of graphs is an important content in modern algebraic graph theory. In this programme, we will investigate the distance and distance (signless) Laplacian spectra of graphs and related topics, including the properties for distance eigenvalues of connected graphs (especially the second largest distance eigenvalue and the least distance eigenvalue), the description of the unique graphs with maximal distance (signless) Laplacian spectral radius among graphs with prescribe parameters, and the related properties for the distance and distance signless Laplacian spreads of graphs.