Geodesic
$D$-equienergetic self-complementary graphs
Kragujevac Journal of Mathematics, Tome 32 (2009) no. 1.

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The $D$-eigenvalues $\{\mu_1,\mu_2,\ldots,\mu_n\} $ of a graph $G$ are the eigenvalues of its distance matrix $D$ and form the $D$-spectrum of $G$ denoted by $spec_D(G)$. The $D$-energy $E_{D}(G)$ of the graph $G$ is the sum of the absolute values of its $D$-eigenvalues. We describe here the distance spectrum of some self-complementary graphs in the terms of their adjacency spectrum. These results are used to show that there exists $D$-equienergetic self-complementary graphs of order $n=48t$ and $24(2t+1)$ for $t\geq 4$. 
@article{KJM_2009_32_1_a11,
     author = {Gopalapillai Indulal and Ivan Gutman},
     title = {$D$-equienergetic self-complementary graphs},
     journal = {Kragujevac Journal of Mathematics},
     pages = {123 - 131},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2009},
     zbl = {1199.05089},
     url = {http://geodesic.mathdoc.fr/item/KJM_2009_32_1_a11/}
}
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Gopalapillai Indulal; Ivan Gutman. $D$-equienergetic self-complementary graphs. Kragujevac Journal of Mathematics, Tome 32 (2009) no. 1. http://geodesic.mathdoc.fr/item/KJM_2009_32_1_a11/