Locally s-arc-transitive graphs arising from product action - Giudici, Michael (Ars mathematica contemporanea, 2023)
We study locally ?$s$?-arc-transitive graphs arising from the quasiprimitive product action (PA). We prove that, for any locally ?$(G,2)$?-arc-transitive graph with ?$G$? acting quasiprimitively with type PA on both ?$G$?-orbits of vertices, the group ?$G$? does not act primitively on either orbit. Moreover, we construct the first examples of locally ?$s$?-arc-transitive graphs of PA type that are not standard double covers of ?$s$?-arc-transitive graphs of PA type, answering the existence question for these graphs.
Keywords: kvaziprimitivna grupa; locally s-arc-transitive graph; lokalno s-ločno tranzitiven graf; product action; produktno delovanje; quasiprimitive group