On cubic non-Cayley vertex-transitive graphs
In 1983, the second author [D. Marui?, Ars Combinatoria 16B (1983), 297302] asked for which positive integers n there exists a non-Cayley vertex-transitive graph on n vertices. (The term non-Cayley numbers has later been given to such integers.) Motivated by this problem, Feng [Discrete Math 248 (2002), 265269] asked to determine the smallest valency ?(n) among valencies of non-Cayley vertex-transitive graphs of order n. As cycles are clearly Cayley graphs, ?(n)?3 for any non-Cayley number n.
vertex-transitive graph non-cayley graph automorphism group