The locally 2-arc transitive graphs admitting a Ree simple group. (English) Zbl 1058.05034
Summary: Three infinite families of locally 2-arc transitive graphs are constructed, which are vertex-intransitive, regular and all vertex stabilizers are conjugate. To the best of our knowledge these are the first infinite families of graphs with these properties. In particular, they are semi-symmetric. It is then shown that the only locally 2-arc transitive graphs admitting a Ree simple group are (i) the graphs in these three families, (ii) (vertex-transitive) 2-arc transitive graphs admitting a Ree simple group, previously classified by the first and third authors, and (iii) standard double covers of the graphs in (ii). This is the first complete classification of locally 2-arc transitive graphs for an infinite family of simple groups.
MSC:
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
| 20D06 | Simple groups: alternating groups and groups of Lie type |
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