Vertex-transitive Graphs On Fewer Than 48 Vertices

<p><strong><em>Vertex-transitive Graphs On Fewer Than 48 Vertices</em></strong></p> <p>This dataset contains all the vertex-transitive graphs on 10-47 vertices.</p> <p>It consists of a collection of tar files, with names like</p> <p>alltrans26.tar</p> <p>meaning that this tar file contains all the vertex-transitive graphs on 26 vertices.</p> <p>Once the tar file is unpacked (using &quot;tar xf alltrans26.tar&quot;) this will create a number of smaller gzipped files with names such as</p> <p>alltrans26_k=03.gz</p> <p>meaning that this file contains all the transitive graphs on 26 vertices with degree (valency) 3.&nbsp;</p> <p>Once the gzip file is unpacked using &quot;gunzip alltrans26_k=03.gz&quot; the resulting file contains all the graphs, one per line, in graph6 format (this format was invented by Brendan McKay and is recognised by SageMath).&nbsp;</p> <p>The first five lines of the file alltrans26_k=03 are as follows:</p> <pre>Ys???C????_CA?@?`?_GO?c?@_?Q??K??O@CG?aA?GAG@?OCCG?GGC?? Ys??WO@?O??O?J?E?A_H??A?C??O?????_?DC?AQ?AAA??oG?C_O?I?? Ys??WWG@?@?A?W?c??g?S?@??G???G??O??S??I?_?Ac??SS??OW??_? Ys?GGSG@?@?A?W?c??g?S?@??G???G??O??S??I?_?Ac??SS??OW??_? Ys?GOO?????c?Q?c?B?@_?I?A??G??A?@?CCC?OP?CCC?C_O?AOC?C_? </pre> <p>These can be directly used as input to SageMath with commands such as</p> <p>g = Graph(&quot;Ys???C????_CA?@?`?_GO?c?@_?Q??K??O@CG?aA?GAG@?OCCG?GGC??&quot;)</p> <p>No attempt has been made to reduce data storage by removing redundancy. So the tar file for vertex-transitive graphs on n vertices contains files for each feasible valency from 0 to n-1, despite the redundancy inherent in storing both a graph and its complement,&nbsp;and in storing both disconnected and connected graphs.</p> <p>&nbsp;</p>