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Graph families defined by their automorphisms
distance-transitive
→
distance-regular
←
strongly regular
↓
symmetric (arc-transitive)
←
t
-transitive,
t
≥ 2
skew-symmetric
↓
(if connected)
vertex- and edge-transitive
→
edge-transitive and regular
→
edge-transitive
↓
↓
↓
vertex-transitive
→
regular
→
(if bipartite)
biregular
↑
Cayley graph
←
zero-symmetric
asymmetric
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