Difference between revisions of "Template:Graph families defined by their automorphisms"
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<table class="infobox" | <table class="infobox" | ||
cellspacing="5" style="width:18.8em; text-align:center; font-size:88%; line-height:1.5em; "> | cellspacing="5" style="width:18.8em; text-align:center; font-size:88%; line-height:1.5em; "> | ||
| − | <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 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> | + | <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> | + | <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, ''t'' ≥ 2]]</td></tr> | + | <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, ''t'' ≥ 2]]</td></tr> |
| − | <tr><td><math>\downarrow</math | + | <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> | + | <tr><td style="vertical-align:middle;"><sub>(if 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> | + | <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 bipartite)</sub><br/>[[biregular graph|biregular]]</td></tr> | + | <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 bipartite)</sub><br/>[[biregular graph|biregular]]</td></tr> |
| − | <tr><td><math>\uparrow</math></td><td></td><td></td></tr> | + | <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> | ||
</table><!-- | </table><!-- | ||
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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 graph | skew-symmetric | asymmetric | ||