Preprint
Jul 2026
Generalized Nordhaus--Gaddum Inequalities for Eigenvalues
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 prove that for all looped graphs $G$ on $n$ vertices, \[\lambda_1(G) + \lambda_2(\overline{G}) \le \frac87 n. \] Our method also gives a short new proof of the Nordhaus-Gaddum result for the spect...
Sahil Agarwal, Carter Antley, Joseph Aulenbacher et al.
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