论文标题
迭代线图只有负征值$ -2 $，它们的补充和能量
Iterated line graphs with only negative eigenvalues $-2$, their complements and energy
论文作者
论文摘要
在光谱图理论中，具有所有相等的负或特征值的图形是特殊的。在本文中，几个迭代的线图$ \ MATHCAL {l}^k（g）$，所有相等的负特征值$ -2 $以$ k \ ge 1 $为特征，并提出了它们的能量后果。同样，这些图的光谱和补体的能量也是如此，有趣的是，它们完全具有两个具有不同多重性的正征值。此外，我们表征了一大批Equienergetic图，这些图表概括了一些现有结果。定义了两个不同的矩阵定义为$ h $ -join（广义组成）的常规图表，以找到邻接矩阵的频谱（部分），laplacian矩阵和无明显的laplacian矩阵，已经证明，这两个标准具有相同图形的相同图形谱。
The graphs with all equal negative or positive eigenvalues are special kind in the spectral graph theory. In this article, several iterated line graphs $\mathcal{L}^k(G)$ with all equal negative eigenvalues $-2$ are characterized for $k\ge 1$ and their energy consequences are presented. Also, the spectra and the energy of complement of these graphs are obtained, interestingly they have exactly two positive eigenvalues with different multiplicities. Moreover, we characterize a large class of equienergetic graphs which generalize some of the existing results. There are two different quotient matrices defined for an equitable partition of $H$-join (generalized composition) of regular graphs to find the spectrum (partial) of adjacency matrix, Laplacian matrix and signless Laplacian matrix, it has been proved that these two quotient matrices give the same respective spectrum of graphs.
