论文标题
在$a_α$和$rd_α$矩阵上
On the $A_α$ and $RD_α$ matrices over certain groups
论文作者
论文摘要
有限组的$ g = p（ω）$ $ g = p（ω）$ $ω$是顶点套装$ω$的图形，两个dertices $ u，v \ inω$在ω$中形成边缘，并且仅当一个是另一个是另一个的积分幂时。令$ d（g）$，$ a（g）$，$ rt（g）$和$ rd（g）$表示对角度矩阵，邻接矩阵，顶点互惠变速器的对角线矩阵和功率图$ G $的Harary Matrix。然后，$a_α$和$rd_α$ $ g $的矩阵定义为$a_α（g）=αd（g） +（1-α）a（g）$和$rd_α（g）=αrt（g） +（1-α）rd（g）rd（g）$。在本文中，我们确定了$a_α$的特征值和$rd_α$矩阵的组$ \ mathcal {g} = \ langle s，r \，：r^{2^kp} = s^s^2 = e，此外，我们计算其远处和提升距离度序列，度量维度和强度度度。
The power graph $G = P(Ω)$ of a finite group $Ω$ is a graph with the vertex set $Ω$ and two vertices $u, v \in Ω$ form an edge if and only if one is an integral power of the other. Let $D(G)$, $A(G)$, $RT(G)$, and $RD(G)$ denote the degree diagonal matrix, adjacency matrix, the diagonal matrix of the vertex reciprocal transmission, and Harary matrix of the power graph $G$ respectively. Then the $A_α$ and $RD_α$ matrices of $G$ are defined as $A_α(G) = αD(G) + (1-α)A(G)$ and $RD_α(G) = αRT(G) + (1-α)RD(G)$. In this article, we determine the eigenvalues of $A_α$ and $RD_α$ matrices of the power graph of group $ \mathcal{G} = \langle s,r \, : r^{2^kp} = s^2 = e,~ srs^{-1} = r^{2^{k-1}p-1}\rangle$. In addition, we calculate its distant and detotar distance degree sequences, metric dimension, and strong metric dimension.
