On Semisymmetric Cubic Graphs of Order 20p², p Prime

A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be an arbitrary prime. Folkman proved [Regular line-symmetric graphs, J. Combin. Theory 3 (1967) 215–232] that there is no semisymmetric graph of order 2p or 2p². In this paper an extension of his result in the case of cubic graphs of order 20p² is given. We prove that there is no connected cubic semisymmetric graph of order 20p² or, equivalently, that every connected cubic edge-transitive graph of order 20p² is necessarily symmetric.