Abstract :
Marušič (Ann. Discrete Math. 27 (1985) 115) proved that all vertex-transitive graphs of order pk are Cayley graphs for each prime p and k=1,2, or 3, and constructed a non-Cayley vertex-transitive graph of order pk and valency 2p+2 for each prime p⩾5 and k⩾4. McKay and Praeger (J. Austral. Math. Soc. (A) 56 (1994) 53) gave an alternative construction of a non-Cayley vertex-transitive graph of order pk for each prime p⩾3 and k⩾4. In this paper it is proved that, for each positive integer k and each prime p⩾3, a vertex-transitive graph of order pk with valency less than 2p+2 is a Cayley graph.
