Some new results on anti-adjacency spectra of regular graphs

The anti-adjacency matrix [Formula: see text] of a simple graph [Formula: see text] with [Formula: see text], is a square matrix of order [Formula: see text] with rows and columns indexed by [Formula: see text], where the [Formula: see text]-entry [Formula: see text] is [Formula: see text], if the vertices [Formula: see text] and [Formula: see text] are not adjacent to each other and [Formula: see text], otherwise. The [Formula: see text]- entry of [Formula: see text] is [Formula: see text]. The anti-adjacency eigenvalues of [Formula: see text] are the eigenvalues obtained from the matrix [Formula: see text] and the corresponding spectra is called the anti-adjacency spectra of [Formula: see text], denoted by [Formula: see text]-spec([Formula: see text]). In this paper, we discuss the anti-adjacency spectra of join and disjoint union of regular graphs. The anti-adjacency spectra of bipartite regular graphs, line graphs of regular graphs and strongly regular graphs are also discussed.