@article{3a0e1f9a1b9e45a091da02c971f1f862,
title = "The praeger-xu graphs: Cycle structures, maps, and semitransitive orientations",
abstract = "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.",
keywords = "Cycle structure, Graph, Reflexible, Regular map, Rotary map, Semitransitive, Transitive",
author = "R. Jajcay and P. Poto{\v c}nik and S. Wilson",
note = "Funding Information: Received August 1, 2018; revised April 5, 2019. 2010 Mathematics Subject Classification. Primary 20B25. Key words and phrases. Graph; transitive; cycle structure; semitransitive; regular map; rotary map; reflexible. Robert Jajcay supported in part by VEGA 1/0596/17, VEGA 1/0719/18, APVV-15-0220, by the Slovenian Research Agency (research projects N1-0038, N1-0062, J1-9108), and by NSFC 11371307. Primoˇz Potoˇcnik supported in part by the Slovenian Research Agency program P1-0294 and both Primoˇz Potoˇcnik and Steve Wilson acknowledge the support of the bilateral grant BI-US/16-17-031. Publisher Copyright: {\textcopyright} 2019, Univerzita Komenskeho. All rights reserved.",
year = "2019",
month = jun,
day = "26",
language = "English (US)",
volume = "88",
pages = "269--291",
journal = "Acta Mathematica Universitatis Comenianae",
issn = "0862-9544",
publisher = "Univerzita Komenskeho",
number = "2",
}