Let G be a graph with order n and \(\overline{G}\) be its complement. In 1956, Nordhaus and Gaddum showed that \(2\sqrt{n}\leqslant \chi (G)+\chi (\overline{G})\leqslant n+1\) and \(n\leqslant \chi (G)\chi (\overline{G})\leqslant (n+1)^{2}/4\) , where \(\chi (G)\) and \(\chi (\overline{G})\) are the chromatic numbers of G and \(\overline{G}\) , respectively. The Nordhaus–Gaddum-type problems focus on the sum or product of some invariants of a graph and its complement. In this paper, we introduce an edge-shift operation and determine the extremal hypergraphs, which attain the extremal value of the sum of spectral radius or transversals for a uniform hypergraph and its complement. The spectral radius is the maximal absolute value of eigenvalues of the adjacency tensor of a hypergraph, and transversal number is the minimum cardinality of a vertex subset, which has a nonempty intersection with each edge. Furthermore, we also discuss some relations between spectral invariants and transversal numbers of uniform hypergraphs.
