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New locally 9-arc-transitive graphs!

July 7, 2011

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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2 Comments leave one →
  1. Michael Giudici permalink
    July 7, 2011 6:21 pm

    I should add that the new examples all have valency {3,5}.

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