Template:Graph families defined by their automorphisms

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Revision as of 17:46, 17 August 2015 by imported>David Eppstein (Undid revision 676504002 by Maproom (talk) "n" is a really bad choice of variable for graph theory, where it invariably means "number of vertices")
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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 ≥ 2skew-symmetric
<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 graph<math>\boldsymbol{\leftarrow}</math>zero-symmetricasymmetric