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


  • Aliyu, I.K. 1Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Nigeria
  • Aliyu, I.S. Department of Mathematics, Air Force Institute of Technology, Kaduna, Nigeria.


Adjacency energy, energy of graph, maximum degree energy, ring of integers modulo n, Seidel energy


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 (ℤn), 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.




How to Cite

Aliyu, I.K., & Aliyu, I.S. (2021). Energy of the Zero-Divisor Graph of the Integers Modulo n (ℤn). Academy Journal of Science and Engineering, 15(1), 22–33. Retrieved from