Geodesic
The Praeger-Xu graphs: Cycle structures, maps and semitransitive orientations
Robert Jajcay1 ; Primož Potočnik2 ; Steve Wilson3 ; Robert Jajcay ; Primož Potočnik ; Steve Wilson
1Faculty of Mathematics, Physics and Computer Science, Comenius University, Bratislava, Slovakia
2Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
3Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ, USA
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 2, pp. 269-291 
Robert Jajcay; Primož Potočnik; Steve Wilson; Robert Jajcay; Primož Potočnik; Steve Wilson. The Praeger-Xu graphs:  Cycle structures, maps and semitransitive orientations. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 2, pp. 269-291. http://geodesic.mathdoc.fr/item/AMUC_2019_88_2_a8/
@article{AMUC_2019_88_2_a8,
     author = {Robert Jajcay and Primo\v{z} Poto\v{c}nik and Steve Wilson and Robert Jajcay and Primo\v{z} Poto\v{c}nik and Steve Wilson},
     title = { The {Praeger-Xu} graphs:  {Cycle} structures, maps and semitransitive orientations},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {269--291},
     year = {2019},
     volume = {88},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_2_a8/}
}
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Voir la notice de l'article provenant de la source Comenius University

We consider tetravalent graphs within a family introduced by Praeger and Xu in 1989. These graphs have the property of having exceptionally large symmetry groups among all tetravalent graphs. This very property makes them unsuitable for the use of simple computer techniques. We apply techniques from coding theory to determine for which values of the parameters the graphs allow cycle structures, semitransitive orientations, or rotary maps; all without recourse to the use of computers.