Document Type : Research Paper

**Author**

Department of Mathematics, St.Aloysius College, Edathua, Alappuzha, India

**Abstract**

The D-eigenvalues {µ_{1},…,µ_{p}} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, E_{D}(G) of G is given by E_{D} (G) =∑_{i=1}^{p} |µ_{i}|. 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_{D}(\overline{L^{k}(G)}), k≥2 depends only on p and r. This result leads to the construction of regular D-equi energetic pair of graphs.

**Keywords**

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February 2017

Pages 51-56