Difference between revisions of "Template:Graph families defined by their automorphisms"
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imported>Cedar101 m ({{nowrap}}) |
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| − | + | {| 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;" | → | |
| − | + | | style="vertical-align: middle;" | [[distance-regular graph|distance-regular]] | |
| − | + | ! style="vertical-align: middle;" | ← | |
| − | + | | style="vertical-align: middle;" | [[strongly regular graph|strongly regular]] | |
| − | + | |- | |
| − | + | ! ↓ | |
| − | + | | | |
| − | + | | | |
| − | + | |- | |
| − | + | | style="vertical-align: middle;" | [[symmetric graph|symmetric (arc-transitive)]] | |
| + | ! style="vertical-align: middle;" | ← | ||
| + | | style="vertical-align: middle;" | [[symmetric graph|{{nowrap|''t''-transitive,}} {{math|size=100%|''t'' ≥ 2}}]] | ||
| + | | | ||
| + | | [[Skew-symmetric graph|skew-symmetric]] | ||
| + | |- | ||
| + | ! ↓ | ||
| + | | | ||
| + | | | ||
| + | | | ||
| + | | | ||
| + | |- | ||
| + | | style="vertical-align: middle;" | <sub>(if connected)</sub><br />[[half-transitive graph|vertex- and edge-transitive]] | ||
| + | ! style="vertical-align: middle;" | → | ||
| + | | style="vertical-align: middle;" | [[semi-symmetric graph|edge-transitive and regular]] | ||
| + | ! style="vertical-align: middle;" | → | ||
| + | | style="vertical-align: middle;" | [[edge-transitive graph|edge-transitive]] | ||
| + | |- | ||
| + | ! ↓ | ||
| + | | | ||
| + | ! ↓ | ||
| + | | | ||
| + | ! ↓ | ||
| + | |- | ||
| + | | style="vertical-align: middle;" | [[vertex-transitive graph|vertex-transitive]] | ||
| + | ! style="vertical-align: middle;" | → | ||
| + | | style="vertical-align: middle;" | [[regular graph|regular]] | ||
| + | ! style="vertical-align: middle;" | → | ||
| + | | style="vertical-align: middle;" | <sub>(if bipartite)</sub><br />[[biregular graph|biregular]] | ||
| + | |- | ||
| + | ! ↑ | ||
| + | | | ||
| + | | | ||
| + | |- | ||
| + | | style="vertical-align: middle;" | [[Cayley graph]] | ||
| + | ! style="vertical-align: middle;" | ← | ||
| + | | style="vertical-align: middle;" | [[Zero-symmetric graph|zero-symmetric]] | ||
| + | | | ||
| + | | [[Asymmetric graph|asymmetric]] | ||
| + | |} | ||