Products of graphs and Nordhaus-Gaddum type inequalities for eigenvalues

Abstract

In this paper, we obtain α as coefficient for the G = Kαn∪K(1−α)n and by which we discuss Nikiforov’s conjecture for λ1 and Aouchiche and Hansen’s conjecture for q1 in Nordhaus-Gaddum type inequalities. Furthermore, by the properties of the products of graphs we put forward a new approach to find some bounds of Nordhaus-Gaddum type inequalities.