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Question

任何一个图都可以用矩阵（邻接矩阵、Laplace矩阵等）来表示，并可通过矩阵的特征值（图谱）来研究图的结构及性质。本文主要讨论具有固定割点数的无割边连通图的谱问题。根据无割边连通图的性质特点及其邻接矩阵最大特征值的变化规律，利用移接变形，给出了割点数不超过2的无割边连通图的谱半径达到最大的极图。

Answer 1

Any graph can be expressed by a matrix (adjacency matrix, Laplace matrix), and its structure and properties can be studied through the eigenvalue (graph spectrum) of the matrix. This paper mainly discusses the spectral problems of the no cutting edge connected graph with fixed cutting points. By using graft transformation, and basing on the property traits of no cutting edge connected graph and the variable law of the adjacency matrix’s optimum eigenvalue, this paper comes out with a spectral radius’ biggest extreme graph of no cutting edge connected graph with a fixed cutting points of not more than 2.

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