International Journal For Multidisciplinary Research

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A Widely Indexed Open Access Peer Reviewed Multidisciplinary Bi-monthly Scholarly International Journal

Call for Paper Volume 7, Issue 4 (July-August 2025) Submit your research before last 3 days of August to publish your research paper in the issue of July-August.

Laplacian Energy of Zn-graph

Author(s) Dr. Jimly Manuel
Country India
Abstract 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 .
Keywords Distance Matrix, Laplacian Matrix, Laplacian Spectrum, Laplacian Energy.
Field Mathematics
Published In Volume 7, Issue 4, July-August 2025
Published On 2025-08-03
DOI https://doi.org/10.36948/ijfmr.2025.v07i04.52707
Short DOI https://doi.org/g9vzj7

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