恰有三个主特征值的树

Trees with exactly three main eigenvalues

设λ是图G的一个特征值,如果存在属于λ的一个特征向量X=(x1,x2,…,xn)T,使得∑nk=1xk≠0,则称λ是图G的主特征值。通过讨论图的主特征值数与公平划分之间的联系,给出某些具有三个主特征值的树类及其主特征值的计算方法。

An eigenvalue of graphs is called a main eigenvalue if it has an eigenvector the sum of whose entries is not zero. By studying the relationship between the main eigenvalue and the equitable partition of graphs, it gives some trees with exactly three main eigenvalues and computing method of main eigenvalues.