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. 
@article{KJM_2010_34_1_a14,
     author = {Kumarappan Kathiresan and R. Sumathi},
     title = {Radial {Digraphs}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {161 - 170},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     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/