For any positive integer n divisible by 3, let k divide n and  Taking  as the set of moduli, we define a graph with the vertices  and an edge between any two vertices x and y if and only if  for  We label this graph as  We enumerate triangles and the number of components of the proposed graph. Further, we find the independence number, clique number, spectrum, Laplacian spectrum, energy and Laplacian energy of the proposed graph. Finally, we prove that the proposed graphs can be reduced to path graphs by substituting the moduli set.

vertex degrees, graphs, congruences, set of moduli, Laplacian

Received: October 8, 2024; Accepted: November 22, 2024; Published: December 14, 2024

How to cite this article: Sufyan Asif and M. Khalid Mahmood, Structural properties of the graphs arising from congruences over set of moduli, JP Journal of Algebra, Number Theory and Applications 64(1) (2025), 81-98. https://doi.org/10.17654/0972555525005

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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