Trivalent dihedrants and bi-dihedrants
Abstract
A Cayley (resp. bi-Cayley) graph on a dihedral group is called a {\em dihedrant} (resp. {\em bi-dihedrant}). In 2000, a classification of trivalent arc-transitive dihedrants was given by Maru\v si\v c 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].
- Publication:
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arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.09367
- arXiv:
- arXiv:1906.09367
- Bibcode:
- 2019arXiv190609367Z
- Keywords:
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- Mathematics - Combinatorics