Trivalent dihedrants and bi-dihedrants

A Cayley (resp. bi-Cayley) graph on a dihedral group is called dihedrant bi-dihedrant). In 2000, classification of trivalent arc-transitive dihedrants was given by Marušič and Pisanski, several years later, non-arc-transitive order 4p or 8p (p prime) were classified Feng et al. As generalization these results, our first result presents dihedrants. Using this, complete vertex-transitive non-Cayley bi-dihedrants given, thus completing the study initiated in previous paper [Discrete Math. 340 (2017) 1757–1772]. by-product, we generalize theorem [The Electronic Journal Combinatorics 19 (2012) #P53].