On the $\alpha$-index of minimally $k$-(edge-)connected graphs for small $k$

Jiayu Lou, Ligong Wang, Ming Yuan

Let $G$ be a graph with adjacency matrix $A(G)$ and let $D(G)$ be the diagonal matrix of vertex degrees of $G$. For any real $\alpha \in [0,1]$, Nikiforov defined the $A_{\alpha }$-matrix of a g…