On the $A_{\alpha }$-spectra of some join graphs

Mainak Basunia, Iswar Mahato, M. Rajesh Kannan

Let $G$ be a simple, connected graph and let $A(G)$ be the adjacency matrix of $G$. If $D(G)$ is the diagonal matrix of the vertex degrees of $G$, then for every real $\alpha \in [0,1]$,…