Template:Graph families defined by their automorphisms

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Graph families defined by their automorphisms
distance-transitive<math>\boldsymbol{\rightarrow}</math>distance-regular<math>\boldsymbol{\leftarrow}</math>strongly regular
<math>\boldsymbol{\downarrow}</math>
symmetric (arc-transitive)<math>\boldsymbol{\leftarrow}</math>t-transitive, t ≥ 2
<math>\boldsymbol{\downarrow}</math>
(if connected)
vertex- and edge-transitive
<math>\boldsymbol{\rightarrow}</math>edge-transitive and regular<math>\boldsymbol{\rightarrow}</math>edge-transitive
<math>\boldsymbol{\downarrow}</math><math>\boldsymbol{\downarrow}</math><math>\boldsymbol{\downarrow}</math>
vertex-transitive<math>\boldsymbol{\rightarrow}</math>regular<math>\boldsymbol{\rightarrow}</math>(if bipartite)
biregular
<math>\boldsymbol{\uparrow}</math>
Cayley graphskew-symmetricasymmetric