In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product of the chromatic number of a graph and its complement, in terms of the order of the graph. Since then, relations of a similar type have been proposed for many other graph invariants, in several hundred papers. We present a survey on this research endeavor. © 2011 Elsevier B.V. All rights reserved.
Aouchiche, M., & Hansen, P. (2013). A survey of Nordhaus-Gaddum type relations. In Discrete Applied Mathematics (Vol. 161, pp. 466–546). https://doi.org/10.1016/j.dam.2011.12.018