A connection between the $A_{\alpha }$-spectrum and the Lovász theta number

Gabriel Coutinho, Thiago Oliveira

We show that the smallest $\alpha$ so that $\alpha D+(1-\alpha )A\succcurlyeq 0$ is at least $1/\vartheta (\overline{G})$, significantly improving upon a result due to Nikiforov and Rojo (2017).…