论文标题
在$a_α$ -matrix的特征多项式上，用于某些图的操作
On the characteristic polynomial of the $A_α$-matrix for some operations of graphs
论文作者
论文摘要
令G为订单$ n $，带有邻接矩阵$ a（g）$和对角矩阵的$ d（g）$。对于[0,1] $中的每个$α\，Nikiforov \ cite {vn17}定义了矩阵$a_α（g）=αd（g） +（1-α）a（g）$。在本文中，我们介绍$a_α（g）$ - 特征多项式时，当通过合并两个图获得$ g $时，如果$ g $是半规则的两部分图，我们将获得与$ g $相关的line-characteristic characteristic characteristic characteristic characteristic characteristic chum。此外，如果$ g $是常规图，我们将展示$a_α$ - 特征性的多项式，用于从某些操作中获得的图。
Let G be a graph of order $n$ with adjacency matrix $A(G)$ and diagonal matrix of degree $D(G)$. For every $α\in [0,1]$, Nikiforov \cite{VN17} defined the matrix $A_α(G) = αD(G) + (1-α)A(G)$. In this paper we present the $A_α(G)$-characteristic polynomial when $G$ is obtained by coalescing two graphs, and if $G$ is a semi-regular bipartite graph we obtain the $A_α$-characteristic polynomial of the line graph associated to $G$. Moreover, if $G$ is a regular graph we exhibit the $A_α$-characteristic polynomial for the graphs obtained from some operations.
