A Study on Anti-Adjacency Spectra of Graphs

Let [Formula: see text] be a simple undirected graph with vertex set [Formula: see text] and edge set [Formula: see text]. The anti-adjacency matrix of [Formula: see text], denoted by [Formula: see text], is the [Formula: see text] matrix, whose rows and columns are indexed by [Formula: see text], where each [Formula: see text]-entry of the matrix is [Formula: see text], if there is no edge between the corresponding vertices [Formula: see text] and [Formula: see text] and [Formula: see text], otherwise. The [Formula: see text]-entry of [Formula: see text] is [Formula: see text], for [Formula: see text]. The eigenvalues of [Formula: see text] represent the anti-adjacency eigenvalues of [Formula: see text]. We denote the corresponding spectra by [Formula: see text]-spec([Formula: see text]). In this paper, we discuss the anti-adjacency spectra of some fundamental graph classes.