Semisymmetry and half-arc-transitive group actions
by
Primož Potočnik
University of Ljubljana
Coauthors: Dragan Marušič

Let X be a regular graph and G <= AutX. If G acts transitively on vertex-set and on edge-set of X, but not transitively on arc-set of X, then X is said to be (G, ¹/₂)-arc-transitive. Similarly, if G acts transitively on edge-set, but not on vertex-set of X, then X is said to be G-semisymmetric. These two families of graphs have been studied extensively in last few decades, but (to the author's best knowledge) no connection between the two of them has been established. A construction of a semisymmetric graph (generalizing the original Folkman's construction), arising from a (H, ¹/₂)-arc-transitive graph X, which is also G-arc-transitive for some groups H <= G <= \aut X, H of index 2 in G, will be presented in the talk.

Date received: November 30, 2000