Weakly Flag-transitive Configurations and Half-arc-transitive Graphs

A configuration is weakly flag-transitive if its group of automorphisms acts intransitively on flags but the group of all automorphisms and anti-automorphisms acts transitively on flags. It is shown that weakly flag-transitive configurations are in one-to-one correspondence with bipartite12-arc-transitive graphs of girth not less than 6. Several infinite families of weakly flag-transitive configurations are given via their Levi graphs. Among others an infinite family of non-self-polar weakly flag-transitive configurations is constructed. The smallest known weakly flag-transitive configuration has 27 points and the smallest known non-self-polar weakly flag-transitive configuration has 34 points.