论文标题
在链图的Seidel矩阵的光谱和能量上
On the spectrum and energy of Seidel matrix for chain graphs
论文作者
论文摘要
我们研究了连接链图的Seidel矩阵$ S $的各种光谱特性。我们证明，$ -1 $始终是$ s $的特征值，所有其他$ s $的特征值最多都可以具有多重性。我们获得Seidel特征值$ -1 $的多样性，最小数量的不同特征值，特征值边界，特征多项式，链图Seidel能量的上限和上限。还表明，此处获得的能量边界比出血者猜想的边界更好。我们还获得了一些订单$ n $的特殊连锁图的最小塞德尔能量。我们还提供了许多开放问题。
We study various spectral properties of the Seidel matrix $S$ of a connected chain graph. We prove that $-1$ is always an eigenvalue of $S$ and all other eigenvalues of $S$ can have multiplicity at most two. We obtain the multiplicity of the Seidel eigenvalue $-1$, minimum number of distinct eigenvalues, eigenvalue bounds, characteristic polynomial, lower and upper bounds of Seidel energy of a chain graph. It is also shown that the energy bounds obtained here work better than the bounds conjectured by Haemers. We also obtain the minimal Seidel energy for some special chain graphs of order $n$. We also give a number of open problems.
