论文标题
在某些组上的功率图的光谱特性上
On the Spectral properties of power graphs over certain groups
论文作者
论文摘要
一个组$ω$的功率图$ p（ω）$是带顶点集$ω$的图形，因此，当两个不同的顶点构成边缘，并且仅当其中一个是另一个的积分力量时。在本文中，我们确定组$ \ Mathcal {g} = \ langle s，r \，：r^{2^kp} = s^2 = e，〜srs^{ - 1} = r^{2^{2^{k-1} p-1} p-1} \ rangle $。此外，我们计算了其特征多项式，用于邻接，拉普拉斯和与此功率图相关的无价laplacian矩阵。此外，我们确定其光谱，拉普拉斯谱和拉普拉斯能量。
The power graph $P(Ω)$ of a group $Ω$ is a graph with the vertex set $Ω$ such that two distinct vertices form an edge if and only if one of them is an integral power of the other. In this article, we determine the power graph of the group $\mathcal{G} = \langle s,r \, : r^{2^kp} = s^2 = e,~ srs^{-1} = r^{2^{k-1}p-1}\rangle$. Further, we compute its characteristic polynomial for the adjacency, Laplacian, and signless Laplacian matrices associated with this power graph. In addition, we determine its spectrum, Laplacian spectrum, and Laplacian energy.
