On Semisymmetric Cubic Graphs of Order 20p2, p Prime

Abstract

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.

Keywords

• edge-transitive graph
• vertex-transitive graph
• semisymmetric graph
• order of a graph
• classification of cubic semisymmetric graphs
• 05e18
• 20d60
• 05c25
• 20b25