Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with related to groups and

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.