Summary: Let \(G\) be a graph with adjacency matrix \(A(G)\) and let \(D(G)\) be the diagonal matrix of the degrees of \(G\). For any real \(\alpha \in [0, 1]\), V. Nikiforov [“Merging the \(A\)-and \(Q\)-spectral theories”, Appl. Anal. Discrete Math. 11, No. 1, 81–107 (2017; doi:10.2298/AADM1701081N)] defined the matrix \(A_\alpha(G)\) as \[ A_\alpha(G) = \alpha D(G) +(1 - \alpha) A(G) . \] The largest eigenvalue of \(A_\alpha(G)\) is called the \(A_\alpha\)-spectral radius of \(G\). In this paper, we give three edge graft transformations on \(A_\alpha\)-spectral radius. As applications, we determine the unique graph with maximum \(A_\alpha\)-spectral radius among all connected graphs with diameter \(d\), and determine the unique graph with minimum \(A_\alpha\)-spectral radius among all connected graphs with given clique number. In addition, some bounds on the \(A_\alpha\)-spectral radius are obtained.