Difference between revisions of "Template:Graph families defined by their automorphisms"
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imported>David Eppstein (oops, repeated entry, fix) |
imported>Maproom (replaced "t-transitive" by "n-transitive". On my system, the "t-" was displayed on a line by itself, and looked like a bit of fly-shit. "n" is a more substantial letter.) |
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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 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>\boldsymbol{\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>\boldsymbol{\leftarrow}</math></td><td style="vertical-align:middle;">[[symmetric graph|'' | + | <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|''n''-transitive, ''n'' ≥ 2]]</td><td></td><td>[[Skew-symmetric graph|skew-symmetric]]</td></tr> |
<tr><td><math>\boldsymbol{\downarrow}</math></td><td></td><td></td><td></td><td></td></tr> | <tr><td><math>\boldsymbol{\downarrow}</math></td><td></td><td></td><td></td><td></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 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> | ||
Revision as of 12:39, 17 August 2015
| 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> | n-transitive, n ≥ 2 | skew-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-symmetric | asymmetric | |