3-一致超图的H-谱半径问题研究

In 2005, Lim and Qi independently proposed the definitions of eigenvalues for higher order tensors. Since then, spectral theory of hypergraphs has developed rapidly. Moreover, the establishment of the Perron-Frobenius theorem has made a theoretical foundation on the spectral theory of hypergraphs. In this project, we are studying the H-spectral radius of 3-uniform hypergraphs, which consists of the following two parts:.1、The lower bound of the H-spectral radius for MV-tree and the ordering .2、The upper bound of the H-spectral radius of the maximal planar 3-uniform hypergraphs.. Spectra theory of hypergraphs is a new topic, where there are many new problems need to be solved. In this project, we are aiming to obtain some new methods on 3-uniform hypergraphs and preparing on the research of the spectral theory of k-uniform hypergraphs.

自2005年，Lim和祁力群教授分别提出张量特征值的概念后，超图的谱理论研究得到了迅速地发展。同时，非负张量的Perron-Frobenius 定理的完善为超图的谱理论研究提供了坚实的理论基础。本项目主要研究3-一致超图的H-谱半径问题，包括以下两个方面：.（1） 研究MV-树邻接H-谱半径的下界以及排序。.（2） 研究极大3-一致可平面超图的邻接H-谱半径的上界，并刻画达到该上界的极图。. 因为超图的张量谱研究是一个新的研究领域，其中有许多问题有待解决。我们希望通过本项目的研究工作，能够在理论研究和方法创新上有所突破，为进一步k-一致超图的谱问题研究奠定研究基础。