A Google search on "transitively orientable graphs" turns up numerous
hits. For example, see the 'Google books' entry by Balakrishnan
(Schaum's Outline); the excerpted page has relevant material. See also
http://www.cs.uoi.gr/~charis/files/MinComp-ISAAC.pdf or
www.alastairfarrugia.net/conv_orient_dam.ps
R.G. Vickson