New locally 9-arc-transitive graphs!

In Michael’s talk at Rogla, he explained that if a graph is locally s-arc-transitive, then s\leqslant 9 (by a result of Stellmacher 1996) and that the only known examples for s=9 came from classical generalised octagons associated with \,^2F_4(2^{2n+1}) and their covers. This question inspired Marston Conder to search for new examples by a cool trick starting from the smallest known example. We will suppress the details for now until Marston has completed his work. Hot off the press, we can tell you that there are

new locally 9-arc-transitive graphs!

They are big and their automorphism groups are alternating groups. More details soon …


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