Laplacian Energy of Zn-graph

In this paper, we investigate the structural and spectral properties of a graph associated with the finite cyclic group , referred to as the . This graph is defined as the underlying simple graph of the digraph constructed using the multiplicative structure of the power digraph of We explore various matrices associated with this graph, including the distance matrix, adjacency matrix, and Laplacian matrix. Special attention is given to the Laplacian spectrum and the Laplacian energy of the . Explicit results are derived for the Laplacian energy of and , where p and q are primes. Our findings highlight interesting relationships between the algebraic properties of and the graph-theoretic properties of its associated .