Laplacian and Wiener index of extension of zero divisor graph.

The main purpose of this paper is to study the Laplacian eigenvalues of the extension of the zero divisor graph, Γ e (Z n) , for some particular values of n. We characterize the values of n that give the equality of the spectral radius and the second-smallest eigenvalue of Γ e (Z n). Finding Wiener index of Γ e (Z n) in terms of its Laplacian eigenvalues is another objective of this paper. [ABSTRACT FROM AUTHOR]