Anti-adjacency and Laplacian spectra of inverse graph of group of integers modulo n

Abstract

Research on the spectra of a graph still attracts the attention of many researchers over the last decades. In addition, research related to graphs obtained from an algebraic structure such as groups and rings is also growing. This paper determines the spectrum of the anti-adjacency and Laplacian matrices of inverse graph of a finite commutative group, namely the addition group of integers modulo n. It can be concluded that all eigenvalues of anti-adjacency and Laplacian matrices of the inverse graph of addition group of integers modulo n are integer