Energy of the Zero-Divisor Graph of the Integers Modulo n (ℤn)

Abstract

Adding the moduli (absolute values) of the eigenvalues of a matrix generated from a graph gives the energy of the graph. Three different types of energies are computed in this paper; the adjacency energy, Seidel energy and the maximum degree energy. The graph under consideration is the zero-divisor graph of the integers modulo n (ℤ_n), where we considered seven rings of integers modulo n, namely, ℤ₆,ℤ₈,ℤ₉,ℤ₁₀,ℤ₁₂,ℤ ₁₄ and ℤ₁₅. The matrices of the graphs are first generated after which the energies are then computed using the eigenvalues of the respective matrices.