Products of graphs and Nordhaus-Gaddum type inequalities for eigenvalues

نویسندگان

1 Department of Computer Science Martin-Luther University Halle-Wittenberg

doi
10.22108/toc.2017.21474
چکیده

In this paper‎, ‎we obtain $\alpha$ as coefficient for the $G=K_{\alpha n} \cup \overline{K_{(1-\alpha)n}}$ and by which we discuss Nikiforov's conjecture for $\lambda_{1}$ and Aouchiche and Hansen's conjecture for $q_1$ 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.