Geodesic
Transitive Orientation of Graphs and Identification of Permutation Graphs
Canadian journal of mathematics, Tome 23 (1971) no. 1, pp. 160-175

Voir la notice de l'article provenant de la source Cambridge University Press

The graphs considered in this paper are assumed to be finite, with no edge joining a vertex to itself and with no two distinct edges joining the same pair of vertices. An undirected graph will be denoted by G or (V, E), where V is the set of vertices and E is the set of edges. An edge joining the vertices i,j ∊ V will be denoted by the unordered pair (i,j).An orientation of G = (V, E) is an assignment of a unique direction i → j or j → i to every edge (i,j) ∊ E. The resulting directed image of G will be denoted by G→ or (V, E→), where E→ is now a set of ordered pairs E→ = {[i,j]| (i,j) ∊ E and i → j}. Notice the difference in notation (brackets versus parentheses) for ordered and unordered pairs. 
Pnueli, A.; Lempel, A.; Even, S. Transitive Orientation of Graphs and Identification of Permutation Graphs. Canadian journal of mathematics, Tome 23 (1971) no. 1, pp. 160-175. doi: 10.4153/CJM-1971-016-5
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