Maxima of the \(A_\alpha\)-spectral Radius of Graphs with Given Size and Minimum Degree \(\delta \ge 2\)

In this paper, we study the \( A_\alpha \)-spectral radius of graphs in terms of given size \( m \) and minimum degree \( \delta \geq 2 \), and characterize the corresponding extremal graphs completely. Furthermore, we characterize extremal graphs having maximum \( A_\alpha \)-spectral radius among (minimally) \( 2 \)-edge-connected graphs with given size \( m \).