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In this paper, we construct two new infinite families of arc-transitive distance-regular graphs, related to Suzuki groups  and Ree groups , where . They are antipodal -covers of complete graphs on  or  vertices, respectively, with  and  being an arbitrary odd divisor of . We also find that the graph on the set of involutions of  with , whose edges are the pairs of involutions  such that , is distance-regular.

journal of algebraic combinatorics

Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with $$\lambda =\mu $$ λ = μ related to groups $$Sz(q)$$ S z ( q ) and $$^2G_2(q)$$ 2 G 2 ( q )