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

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

Latest revision as of 05:38, 4 April 2017