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, Gamma 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 Gamma e ( Z n ). Finding Wiener index of Gamma e ( Z n ) in terms of its Laplacian eigenvalues is another objective of this paper. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.