Distance spectra, distance energy and some of the distance based topological indices of unitary Haar graphs

Let [Formula: see text] and [Formula: see text] be the multiplicative group of the additive group [Formula: see text] of integers modulo [Formula: see text]. The unitary Haar graph [Formula: see text] is a graph with vertex set [Formula: see text] and the edge set [Formula: see text]. In this paper, we first calculate the distance spectra and distance energy of [Formula: see text], and then we show that this graph is distance integral, that is all the eigenvalues of its distance matrix are integers. Also we calculate some of the distance based topological indices of this graph such as Wiener, hyper Wiener, Gutman and Harary index.