Difference between revisions of "Template:Graph families defined by their automorphisms"
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imported>David Eppstein (biregular) |
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<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;">[[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><math>\downarrow</math></td><td></td><td><math>\downarrow</math></td><td></td><td><math>\downarrow</math></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 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;">[[biregular graph|biregular]]</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><math>\uparrow</math></td><td></td><td></td></tr> | <tr><td><math>\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> | ||
Revision as of 08:47, 19 June 2013
| Graph families defined by their automorphisms | ||||
| distance-transitive | <math>\rightarrow</math> | distance-regular | <math>\leftarrow</math> | strongly regular |
| <math>\downarrow</math> | ||||
| symmetric (arc-transitive) | <math>\leftarrow</math> | t-transitive, t ≥ 2 | ||
| <math>\downarrow</math>(if connected) | ||||
| vertex- and edge-transitive | <math>\rightarrow</math> | edge-transitive and regular | <math>\rightarrow</math> | edge-transitive |
| <math>\downarrow</math> | <math>\downarrow</math> | <math>\downarrow</math> | ||
| vertex-transitive | <math>\rightarrow</math> | regular | <math>\rightarrow</math> | (if bipartite) biregular |
| <math>\uparrow</math> | ||||
| Cayley graph | skew-symmetric | asymmetric | ||