A graph is called half-arc-transitive if its full automorphism group acts transitively on vertices and edges, but not on arcs. It is well known that for any prime p there is no half-arc-transitive graph of order p or p2. In 1992, Xu classified half-arc-transitive graphs of order p3 and valency 4. In this paper we classify half-arc-transitive graphs of order p3 and valency 6 or 8. In particular, the first known infinite family of half-arc-transitive Cayley graphs on non-metacyclic p-groups is constructed.
@article{964,
title = {Half-arc-transitive graphs of prime-cube order of small valencies},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {14},
year = {2017},
doi = {10.26493/1855-3974.964.594},
language = {EN},
url = {http://dml.mathdoc.fr/item/964}
}
Wang, Yi; Feng, Yan-Quan. Half-arc-transitive graphs of prime-cube order of small valencies. ARS MATHEMATICA CONTEMPORANEA, Tome 14 (2017) . doi : 10.26493/1855-3974.964.594. http://gdmltest.u-ga.fr/item/964/