Bulletin of the
Korean Mathematical Society BKMS

A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let $p$ be a prime. Folkman proved [J.~Folkman, {\it Regular line-symmetric graphs}, Journal of Combinatorial Theory {\bf 3} (1967), no. 3, 215--232] that no semisymmetric graph of order $2p$ or $2p^2$ exists. In this paper an extension of his result in the case of cubic graphs of order $34p^3$, $p\neq 17$, is obtained.

Keywords: Edge-transitive graph, vertex-transitive graph, semisymmetric graph, order of a graph, classification of cubic semisymmetric graphs

MSC numbers: 05E18, 20D60, 05C25, 20B25