Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Sahil Agarwal, Carter Antley, Joseph Aulenbacher +6

For a graph $G$, let ${\lambda }_1(G)\ge {\lambda }_2(G)\ge \cdots \ge {\lambda }_n(G)$ denote the adjacency eigenvalues of $G$. We investigate the asymptotic maximum of \[ λ_i(G)+λ_j(\overline G) \] for fi…