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

Source 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 andsignless Laplacian energies are always equal and are always an even integer. Meanwhile, the adjacency energy is never an odd integer for n is odd.