On the $\alpha$-index of minimally 2-connected graphs with given order or size

Jiayu Lou, Ligong Wang, Ming Yuan

For any real $\alpha \in [0,1]$, Nikiforov defined the $A_{\alpha }$-matrix of a graph $G$ as $A_{\alpha }(G)=\alpha D(G)+(1-\alpha )A(G)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the diagonal matrix o…