On Spectrum and Energy of Identity Graph for Groupof Integers Modulo n, Zn

Authors

  • Mamika Ujianita Romdhini Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Mataram 83125,
  • Athirah Nawawi
  • Faisal Al-Sharqi
  • Salwa .

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5375

Keywords:

Energy of a graph, Identity graph of a group, Z_n

Abstract

Groups and graphs are two concepts of algebraic mathematics. This paper focuses on group structures that can be expressed in graphs known as identity graphs. We investigate the energy of the identity graph for a group of integers modulo n, Zn, for odd and even n corresponding to adjacency, Laplacian, and signless Laplacian matrices. It can be seen that the Laplacian and
signless Laplacian energies are always equal and are always an even integer. Meanwhile, the adjacency energy is never an odd integer for n is odd.

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

On Spectrum and Energy of Identity Graph for Groupof Integers Modulo n, Zn. (2024). European Journal of Pure and Applied Mathematics, 17(4), 2915-2929. https://doi.org/10.29020/nybg.ejpam.v17i4.5375