The complete split graph K_{⌊n/3⌋} ∨ N_{⌈2n/3⌉} (plus one more when n≡2 mod 3) maximizes ρ(G)+ρ(\bar G) for all n, resolving Stevanović's conjecture.
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Nordhaus-Gaddum inequality for the spectral radius of a graph of order $n$
The complete split graph K_{⌊n/3⌋} ∨ N_{⌈2n/3⌉} (plus one more when n≡2 mod 3) maximizes ρ(G)+ρ(\bar G) for all n, resolving Stevanović's conjecture.