论文标题
受顶点子集约束的图形电晕光谱
Spectra of generalized corona of graphs constrained by vertex subsets
论文作者
论文摘要
在本文中，我们介绍了图表的概括。该构造概括了图形的广义电晕（因此，图形的电晕），图形群，图形的电晕 - vertex细分图和图形图形的电晕 - 边缘细分图。此外，它使得能够将更多的图表变体作为其特殊情况。为了确定邻接的光谱，laplacian和上述图的无标志性拉普拉斯矩阵，我们定义了一个概念，即受索引集约束的基质的冠状冠状，该基质概述了图矩阵的冠状动脉。然后，我们证明了几个与确定该值有关的结果。然后，我们根据邻接的特征多项式以及组成图的特征多项式来确定该图的特征多项式和该图的拉普拉斯矩阵，以及与组成图相关的某些矩阵的冠状矩阵。使用这些，我们得出了上述图表的现有变体的邻接和拉普拉斯矩阵的特征多项式，以及具有一些特殊约束的图表的表演图。
In this paper, we introduce a generalization of corona of graphs. This construction generalizes the generalized corona of graphs (consequently, the corona of graphs), the cluster of graphs, the corona-vertex subdivision graph of graphs and the corona-edge subdivision graph of graphs. Further, it enables to get some more variants of corona of graphs as its particular cases. To determine the spectra of the adjacency, Laplacian and the signless Laplacian matrices of the above mentioned graphs, we define a notion namely, the coronal of a matrix constrained by an index set, which generalizes the coronal of a graph matrix. Then we prove several results pertain to the determination of this value. Then we determine the characteristic polynomials of the adjacency and the Laplacian matrices of this graph in terms of the characteristic polynomials of the adjacency and the Laplacian matrices of the constituent graphs and the coronal of some matrices related to the constituent graphs. Using these, we derive the characteristic polynomials of the adjacency and the Laplacian matrices of the above mentioned existing variants of corona of graphs, and some more variants of corona of graphs with some special constraints.
