Geodesic
Radial Digraphs
Kragujevac Journal of Mathematics, Tome 34 (2010) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The Radial graph of a graph $G$, denoted by $R(G)$, has the same vertex set as $G$ with an edge joining vertices $u$ and $v$ if $d(u, v)$ is equal to the radius of $G$. This definition is extended to a digraph $D$ where the arc $(u, v)$ is included in $R(D)$ if $d(u, v)$ is the radius of $D$. A digraph $D$ is called a Radial digraph if $R(H)=D$ for some digraph $H$. In this paper, we shown that if $D$ is a radial digraph of type 2 then $D$ is the radial digraph of itself or the radial digraph of its complement. This generalizes a known characterization for radial graphs and provides an improved proof. Also, we characterize self complementary self radial digraphs. 
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     author = {Kumarappan Kathiresan and R. Sumathi},
     title = {Radial {Digraphs}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {161 - 170},
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     volume = {34},
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     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/KJM_2010_34_1_a14/}
}
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Kumarappan Kathiresan; R. Sumathi. Radial Digraphs. Kragujevac Journal of Mathematics, Tome 34 (2010) no. 1. http://geodesic.mathdoc.fr/item/KJM_2010_34_1_a14/