Paper Title
Some Discussion on Bounds of Characteristic Roots

In this paper we have established the bounds of the extreme characteristic roots of nlap(G) and sLap(G) by their traces. Also found the bounds for n-th characteristic roots of nLap(G) and sLap(G). Keywords - Characteristic root, Normalized Laplacian matrix, Signless Laplacian matrix. AMS subject classification number: 05C78.