Gopalapillai, I. (2017). D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs. Algebraic Structures and Their Applications, 4(1), 51-56. doi: 10.29252/asta.4.1.51

Indulal Gopalapillai. "D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs". Algebraic Structures and Their Applications, 4, 1, 2017, 51-56. doi: 10.29252/asta.4.1.51

Gopalapillai, I. (2017). 'D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs', Algebraic Structures and Their Applications, 4(1), pp. 51-56. doi: 10.29252/asta.4.1.51

Gopalapillai, I. D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs. Algebraic Structures and Their Applications, 2017; 4(1): 51-56. doi: 10.29252/asta.4.1.51

D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs

^{}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.