A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper, tetravalent one-regular graphs of order 3p², where p is a prime, are classified.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-3, author = {Mohsen Ghasemi}, title = {A classification of tetravalent one-regular graphs of order 3p$^2$}, journal = {Colloquium Mathematicae}, volume = {126}, year = {2012}, pages = {15-24}, zbl = {1258.05048}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-3} }
Mohsen Ghasemi. A classification of tetravalent one-regular graphs of order 3p². Colloquium Mathematicae, Tome 126 (2012) pp. 15-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-1-3/