Difference between revisions of "Template:Graph families defined by their automorphisms"

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<tr><td colspan="5"  style="text-align:center; font-size:125%; font-weight:bold; background: #DD9">[[Graph automorphism#Graph families defined by their automorphisms|Graph families defined by their automorphisms]]</td></tr>
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<tr><td colspan="5"  style="text-align:center; font-size:125%; font-weight:bold; background: #DD9"> [[Graph automorphism#Graph families defined by their automorphisms|Graph families defined by their automorphisms]]</td></tr>
<tr><td style="vertical-align:middle;">[[distance-transitive graph|distance-transitive]]</td><td style="vertical-align:middle;"><math>\rightarrow</math></td><td style="vertical-align:middle;">[[distance-regular graph|distance-regular]]</td><td style="vertical-align:middle;"><math>\leftarrow</math></td><td style="vertical-align:middle;">[[strongly regular graph|strongly regular]]</td></tr>
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<tr><td style="vertical-align:middle;">[[distance-transitive graph|distance-transitive]]</td><td style="vertical-align:middle;"><math>\boldsymbol{\rightarrow}</math></td><td style="vertical-align:middle;">[[distance-regular graph|distance-regular]]</td><td style="vertical-align:middle;"><math>\boldsymbol{\leftarrow}</math></td><td style="vertical-align:middle;">[[strongly regular graph|strongly regular]]</td></tr>
<tr><td><math>\downarrow</math></td><td></td><td></td></tr>
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<tr><td><math>\boldsymbol{\downarrow}</math></td><td></td><td></td></tr>
<tr><td style="vertical-align:middle;">[[symmetric graph|symmetric (arc-transitive)]]</td><td style="vertical-align:middle;"><math>\leftarrow</math></td><td style="vertical-align:middle;">[[symmetric graph|''t''-transitive,&nbsp;''t''&nbsp;≥&nbsp;2]]</td></tr>
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<tr><td style="vertical-align:middle;">[[symmetric graph|symmetric (arc-transitive)]]</td><td style="vertical-align:middle;"><math>\boldsymbol{\leftarrow}</math></td><td style="vertical-align:middle;">[[symmetric graph|''t''-transitive,&nbsp;''t''&nbsp;≥&nbsp;2]]</td></tr>
<tr><td><math>\downarrow</math><sub>(if&nbsp;connected)</sub></td><td></td><td></td></tr>
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<tr><td><math>\boldsymbol{\downarrow}</math></td><td></td><td></td></tr>
<tr><td style="vertical-align:middle;">[[half-transitive graph|vertex- and edge-transitive]]</td><td style="vertical-align:middle;"><math>\rightarrow</math></td><td style="vertical-align:middle;">[[semi-symmetric graph|edge-transitive and regular]]</td><td style="vertical-align:middle;"><math>\rightarrow</math></td><td style="vertical-align:middle;">[[edge-transitive graph|edge-transitive]]</td></tr>
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<tr><td style="vertical-align:middle;"><sub>(if&nbsp;connected)</sub><br/>[[half-transitive graph|vertex- and edge-transitive]]</td><td style="vertical-align:middle;"><math>\boldsymbol{\rightarrow}</math></td><td style="vertical-align:middle;">[[semi-symmetric graph|edge-transitive and regular]]</td><td style="vertical-align:middle;"><math>\boldsymbol{\rightarrow}</math></td><td style="vertical-align:middle;">[[edge-transitive graph|edge-transitive]]</td></tr>
<tr><td><math>\downarrow</math></td><td></td><td><math>\downarrow</math></td><td></td><td><math>\downarrow</math></td></tr>
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<tr><td><math>\boldsymbol{\downarrow}</math></td><td></td><td><math>\boldsymbol{\downarrow}</math></td><td></td><td><math>\boldsymbol{\downarrow}</math></td></tr>
<tr><td style="vertical-align:middle;">[[vertex-transitive graph|vertex-transitive]]</td><td style="vertical-align:middle;"><math>\rightarrow</math></td><td style="vertical-align:middle;">[[regular graph|regular]]</td><td style="vertical-align:middle;"><math>\rightarrow</math></td><td style="vertical-align:middle;"><sub>(if&nbsp;bipartite)</sub><br/>[[biregular graph|biregular]]</td></tr>
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<tr><td style="vertical-align:middle;">[[vertex-transitive graph|vertex-transitive]]</td><td style="vertical-align:middle;"><math>\boldsymbol{\rightarrow}</math></td><td style="vertical-align:middle;">[[regular graph|regular]]</td><td style="vertical-align:middle;"><math>\boldsymbol{\rightarrow}</math></td><td style="vertical-align:middle;"><sub>(if&nbsp;bipartite)</sub><br/>[[biregular graph|biregular]]</td></tr>
<tr><td><math>\uparrow</math></td><td></td><td></td></tr>
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<tr><td><math>\boldsymbol{\uparrow}</math></td><td></td><td></td></tr>
 
<tr><td style="vertical-align:middle;">[[Cayley graph]]</td><td></td><td>[[Skew-symmetric graph|skew-symmetric]]</td><td></td><td>[[Asymmetric graph|asymmetric]]</td></tr>
 
<tr><td style="vertical-align:middle;">[[Cayley graph]]</td><td></td><td>[[Skew-symmetric graph|skew-symmetric]]</td><td></td><td>[[Asymmetric graph|asymmetric]]</td></tr>
 
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Revision as of 05:06, 8 May 2014

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