STRUCTURAL PROPERTIES OF THE GRAPHS ARISING FROM CONGRUENCES OVER SET OF MODULI

For any positive integer divisible by 3 , let divide and . Taking as the set of moduli, we define a graph with the vertices , and an edge between any two vertices and 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.