Cubic s-regular graphs of order 2p(3)

Abstract

A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. Malnic et al. (Discrete Math 274 (2004), 187-198) classified the connected cubic edge-transitive, but not vertex-transitive graphs of order 2p(3) for each prime p. In this article, we determine the s-regularity of all connected cubic symmetric graphs of order 2p(3) for each prime p and each s. (C) 2006 Wiley Periodicals, Inc.