On the Anti-Adjacency Spectra of Regular Graphs

For a graph G with vertex set V(G) = {v1,...,vn}, the anti-adjacency matrix, denoted by A∗(G) is a square matrix of order n with rows and columns indexed by V (G), whose (i,j)− entry (i ̸ = j) is 1, if the vertices vi and vj are not adjacent and 0, otherwise. The diagonal entries of A∗(G) is 1. The eigenvalues obtained from A∗(G) are called the anti-adjacency eigenvalues of the graph G and the corresponding spectra is called the anti-adjacency spectra, denoted by a-spec(G). In this paper, we discuss the anti-adjacency spectra of connected and disconnected regular graphs and their complement graphs