Yazd University Algebraic Structures and Their Applications 2382-9761 4 1 2017 02 01 D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs 51 56 1089 10.22034/as.2017.1089 EN Indulal Gopalapillai Department of Mathematics, St.Aloysius College, Edathua, Alappuzha, India Journal Article 2017 11 30 The D-eigenvalues {µ<sub>1</sub>,…,µ<sub>p</sub>} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, E<sub>D</sub>(G) of G is given by E<sub>D</sub> (G) =∑<sub>i=1</sub><sup>p</sup> |µ<sub>i</sub>|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated line graphs of G are of diameter 2 and that E<sub>D</sub>(\overline{L<sup>k</sup>(G)}), k≥2 depends only on p and r. This result leads to the construction of regular D-equi energetic pair of graphs. Distance spectrum Distance energy Line graphs https://as.yazd.ac.ir/article_1089_78d7d575d5ef4cc6f63444bee6a8aafb.pdf