论文标题
霍夫曼图：新旧计划
The Hoffman program of graphs: old and new
论文作者
论文摘要
Hoffman程序关于与图$ G $相关的任何真实或复杂的方形矩阵$ M $，源于A. J. Hoffman的开创性工作，其限制点的图形频谱半径小于$ \ sqrt {2+ \ sqrt {5}} $。该程序由两个方面组成：查找图形$ M $ spectral Radii的所有可能限制点，并检测所有$ m $ spectral Radius的连接图不会超过固定限制点。在本文中，我们总结了有关该主题的结果，这些结果涉及几个图形矩阵，包括邻接，拉普拉斯式，无价的拉普拉斯式，赫尔米尼亚人的邻接和偏度矩阵。同样，讨论了超图的张量。此外，我们获得了有关霍夫曼计划的新结果，该计划与$a_α$ -matrix有关。还提出了有关此主题的一些其他问题。
The Hoffman program with respect to any real or complex square matrix $M$ associated to a graph $G$ stems from A. J. Hoffman's pioneering work on the limit points for the spectral radius of adjacency matrices of graphs less than $\sqrt{2+\sqrt{5}}$. The program consists of two aspects: finding all the possible limit points of $M$-spectral radii of graphs and detecting all the connected graphs whose $M$-spectral radius does not exceed a fixed limit point. In this paper, we summarize the results on this topic concerning several graph matrices, including the adjacency, the Laplacian, the signless Laplacian, the Hermitian adjacency and skew-adjacency matrix of graphs. As well, the tensors of hypergraphs are discussed. Moreover, we obtain new results about the Hoffman program with relation to the $A_α$-matrix. Some further problems on this topic are also proposed.
