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

From blackwiki
Jump to navigation Jump to search
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.)
Line 4: Line 4:
 
<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|''t''-transitive,&nbsp;''t''&nbsp;≥&nbsp;2]]</td><td></td><td>[[Skew-symmetric graph|skew-symmetric]]</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|''n''-transitive,&nbsp;''n''&nbsp;≥&nbsp;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&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 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>

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 ≥ 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