View source for Template:Graph families defined by their automorphisms

{| class="infobox" cellspacing="5" style="width: 18.8em; text-align: center; font-size: 88%; line-height: 1.5em;"
! 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]]
|-
| style="vertical-align: middle;" | [[distance-transitive graph|distance-transitive]]
! style="vertical-align: middle;" | &rarr;
| style="vertical-align: middle;" | [[distance-regular graph|distance-regular]]
! style="vertical-align: middle;" | &larr;
| style="vertical-align: middle;" | [[strongly regular graph|strongly regular]]
|-
! &darr;
|
|
|-
| style="vertical-align: middle;" | [[symmetric graph|symmetric (arc-transitive)]]
! style="vertical-align: middle;" | &larr;
| style="vertical-align: middle;" | [[symmetric graph|{{nowrap|''t''-transitive,}} {{math|size=100%|''t''&nbsp;≥&nbsp;2}}]]
|
| [[Skew-symmetric graph|skew-symmetric]]
|-
! &darr;
|
|
|
|
|-
| style="vertical-align: middle;" | <sub>(if&nbsp;connected)</sub><br />[[half-transitive graph|vertex- and edge-transitive]]
! style="vertical-align: middle;" | &rarr;
| style="vertical-align: middle;" | [[semi-symmetric graph|edge-transitive and regular]]
! style="vertical-align: middle;" | &rarr;
| style="vertical-align: middle;" | [[edge-transitive graph|edge-transitive]]
|-
! &darr;
|
! &darr;
|
! &darr;
|-
| style="vertical-align: middle;" | [[vertex-transitive graph|vertex-transitive]]
! style="vertical-align: middle;" | &rarr;
| style="vertical-align: middle;" | [[regular graph|regular]]
! style="vertical-align: middle;" | &rarr;
| style="vertical-align: middle;" | <sub>(if&nbsp;bipartite)</sub><br />[[biregular graph|biregular]]
|-
! &uarr;
|
|
|-
| style="vertical-align: middle;" | [[Cayley graph]]
! style="vertical-align: middle;" | &larr;
| style="vertical-align: middle;" | [[Zero-symmetric graph|zero-symmetric]]
|
| [[Asymmetric graph|asymmetric]]
|}