d-spectrum and denergy of complements of iterated line graphs of regular graphs

The deigenvalues {µ1,…,µp} of a graph g are the eigenvalues of its distance matrix d and form its dspectrum. the denergy, ed(g) of g is given by ed (g) =∑i=1p |µi|. two non cospectral graphs with respect to d are said to be dequi energetic if they have the same denergy. in this paper we show that if g is an rregular graph on p vertices with 2r ≤ p 1, then the complements of iterated line graphs of g are of diameter 2 and that ed(overline{lk(g)}), k≥2 depends only on p and r. this result leads to the construction of regular dequi energetic pair of graphs.