Products of graphs and Nordhaus-Gaddum type inequalities for eigenvalues

In this paper‎, ‎we obtain \alpha as coefficient for the G=K_{\alpha n} \cup \overline{K_{(۱-\alpha)n}} and by which we discuss Nikiforov's conjecture for \lambda_{۱} and Aouchiche and Hansen's conjecture for q_۱ 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.

کلیدواژه ها:

Nordhaus-Gaddum inequalities ، extremal graphs ، product of graphs