Geodesic
Trivalent dihedrants and bi-dihedrants
Ars Mathematica Contemporanea, Tome 21 (2021) no. 2, article no. 02, 26 p.

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A Cayley (resp. bi-Cayley) graph on a dihedral group is called a dihedrant (resp. bi-dihedrant). In 2000, a classification of trivalent arc-transitive dihedrants was given by Marušič and Pisanski, and several years later, trivalent non-arc-transitive dihedrants of order 4p or 8p (p a prime) were classified by Feng et al. As a generalization of these results, our first result presents a classification of trivalent non-arc-transitive dihedrants. Using this, a complete classification of trivalent vertex-transitive non-Cayley bi-dihedrants is given, thus completing the study of trivalent bi-dihedrants initiated in our previous paper [Discrete Math. 340 (2017) 1757–1772]. As a by-product, we generalize a theorem in [The Electronic Journal of Combinatorics 19 (2012) #P53].
DOI : 10.26493/1855-3974.2373.c02
Keywords: Cayley graph, non-Cayley, bi-Cayley, dihedral group, dihedrant, bi-dihedrant 
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Mi-Mi Zhang; Jin-Xin Zhou. Trivalent dihedrants and bi-dihedrants. Ars Mathematica Contemporanea, Tome 21 (2021) no. 2, article  no. 02, 26 p. doi : 10.26493/1855-3974.2373.c02. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2373.c02/

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