A connection between the $A_{\hat{I}}\pm$-spectrum and the Lovász theta number

Gabriel Coutinho, Thiago Oliveira

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