Let G be a graph of order $n$ with adjacency matrix $A(G)$ and diagonal matrix of degree $D(G)$. For every $\alpha \in [0,1]$, Nikiforov \cite{VN17} defined the matrix $A_\alpha(G) = \alpha D(G) + (1-\alpha)A(G)$. In this paper we present the $A_{\alpha}(G)$-characteristic polynomial when $G$ is obtained by coalescing two graphs, and if $G$ is a semi-regular bipartite graph we obtain the $A_{\alpha}$-characteristic polynomial of the line graph associated to $G$. Moreover, if $G$ is a regular graph we exhibit the $A_{\alpha}$-characteristic polynomial for the graphs obtained from some operations.
翻译:允许 G 以相邻矩阵 $A( G) $( G) 和度数矩阵 $( G) $( $) 表示顺序 。 对于每 $alpha $[ 0. 1 美元, Nikiforov\ cite{ VN17 } 定义了 $A alpha ( G) =\ alpha D( G) + 1-\ alpha) A( G) 美元 。 在本文中, 当用两张图形加固 $( G) 获得 G 美元时, 如果用 $( $ ), 则用 $( g) 字数多数值表示 。 此外, 如果用 $( $) 是普通图表, 我们从一些操作中获取的图形, 则用 $( ä alpha) $ 多数值表示 。