LAUSR

For $ \alpha \in [0,1]$,  let  $A_{\alpha}(G) = \alpha D(G) +(1-\alpha)A(G)$ be $A_{\alpha}$-matrix,  where  $A(G)$ is the adjacent matrix and $D(G)$ is the diagonal matrix of the degrees of a graph $G$. Clearly, $A_{0} (G)$ is the adjacent matrix and $2 A_{\frac{1}{2}}$ is the signless Laplacian matrix.  A connected graph  is a cactus graph if  any two  cycles of $G$  have at most one common vertex, which is an extension of the tree. We first propose the result for  subdivision graphs, and determine the cacti maximizing $A_{\alpha}$-spectral radius   subject to fixed pendant vertices.  In addition,  the corresponding extremal graphs are provided. As consequences, we determine the graph with the  $A_{\alpha}$-spectral radius among all the cacti with $n$ vertices; we also characterize the $n$-vertex cacti with a perfect matching having the largest $A_{\alpha}$-spectral radius.