On the spectral radius of minimally 2-(edge)-connected graphs with given size

A graph is minimally k-connected (k-edge-connected) if it is k-connected (k-edge-connected) and deleting arbitrary chosen edge always leaves a graph which is not k-connected (k-edge-connected). A classic result of minimally k-connected graph is given by Mader who determined the extremal size of a minimally k-connected graph of high order in 1937. Naturally, for a fixed size of a minimally k-(edge)-connected graphs, what is the extremal spectral radius? In this paper, we determine the maximum spectral radius for the minimally $2$-connected ($2$-edge-connected) graphs of given size, moreover the corresponding extremal graphs are also determined.