Geometric Characterization of Graphs from the Suzuki Chain

Let Σ0,…,Σ6 be the graphs from the Suzuki chain [12]. We classify connected locally Σi graphs Θi + 1 for i = 3, 4, 5. If i = 3, 4 then Θi + 1, is isomorphic to Σi + 1, whereas Θ6 is isomorphic either to Σ6 or to its 3-fold antipodal cover 3Σ6.